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Digitized  by  the  Internet  Archive 

in  2007  with  funding  from 

IVIicrosoft  Corporation 


http://www.archive.org/details/businessarithmetOObookrich 


BUSINESS  ARITHMETIC 


BY 

C.   M.  BOOKMAN 

FORMERLY  HEAD  OF  MATHEMATICS  DEPARTMENT 

HIGH   SCHOOL  OF   COMMERCE 

COLUMBUS,   OHIO 


AMERICAN  BOOK  COMPANY 

NEW  YORK  CINCINNATI  CHICAGO 


Copyright,  1914,  by 
C.  M.   BOOKMAN. 


Copyright,  1914,  in  Great  Britain. 


bookman's  bus.  arith. 
E.  P.  I 


>>:. 


PREFACE 

Strict  conformity  to  modern  conditions  is  the  keynote 
of  this  Business  Arithmetic.  Through  the  elimination  of 
useless  material  the  complete  subject  is  presented  in  a  one- 
term  course. 

Speed,  accuracy,  correct  methods,  —  these  are  the  demands 
of  modern  business  and  they  have  been  fully  met.  Abundant 
oral  and  written  problems,  and  vocational,  agricultural,  and 
manual  training  applications  have  been  provided. 

Profit  is  the  ultimate. goal  of  all  business.  Yet  with  all 
its  systematizing,  modern  business,  until  recently,  figured 
its  profit  on  the  cost  of  an  article  instead  of  on  its  selling 
price. 

The  author  believes  that  the  direct  methods  of  presenta- 
tion, the  rapid  calculation  methods,  the  constant  application 
of  aliquot  parts,  the  use  of  the  equation  in  percentage  calcu- 
lations, the  combining  of  rules  and  explanations,  and  the 
recognition  of  the  latest  method  of  figuring  profits  make 
of  the  Business  Arithmetic  a  distinctly  valuable  equipment 
which  business  men  will  not  fail  to  discover  and  commend. 

Acknowledgments  are  due  to  I.  A.  Garbutt,  of  Cincinnati ; 
H.  T.  McMyler,  of  Cleveland;  F.  H.  Hamm  and  W.  C. 
Humpton,  of  Columbus,  Ohio,  for  valuable  material  and 
criticisms;  and  to  Treman,  King  &  Co.,  of  Ithaca,  N.  Y., 
for  the  Retail  Merchants'  Table. 


e%r\r%r\c:)ij 


TO   THE  PUPIL 

Keep  these  two  things  in  mind  :  It  is  necessary  to  be  acmi- 
rate  ;  it  is  essential  to  be  rapid.  Neither  accuracy  nor  speed 
can  be  acquired  without  practice.  First  learn  the  method, 
then  drill  and  drill  until  you  know  that  your  work  is  right. 
As  you  gain  confidence  in  yourself  yo\x  will  work  faster. 

The  exercises,  drills,  and -problems  in  this  book  are  worth 
to  you  all  the  effort  you  will  put  on  them  ;  they  will  not 
waste  your  time  on  what  you  already  know.  Work  out  the 
exercises,  do  the  drill  work,  think  out  tlie  problems.  There 
are  no  tricks  or  puzzles  to  confuse  you,  and  the  problems  are 
no  harder  than  those  you  will  have  to  solve  later.  Then, 
when  you  enter  business,  you  may  know  that  you  are  better 
fitted  for  it  than  the  average  person. 

Above  all,  don't  be  satisfied  to  do  only  fairly  well  what 
ought  to  be  done  very  well.  Some  one  is  going  to  do  it 
better  than  any  one  else ;  why  not  you  ? 


CONTENTS 


PAOK 


Addition 7 

Subtraction 17 

Multiplication        .        .        . 23 

Division 28 

Miscellaneous  Problems 30 

Properties  of  Numbers .38 

Fractions 43 

Reduction  of  Fractions .44 

Aliquot  Parts 47 

Addition  of  Fractions 51 

Subtraction  of  Fractions 52 

Multiplication  of  Fractions          ....        ...  53 

Division  of  Fractions 58 

Denominate  Numbers .        .63 

Reduction  of  Denominate  Numbers 73 

Addition  and  Subtraction  of  Denominate  Numbers  .        .        .73 

Multiplication  and  Division  of  Denominate  Numbers        .        .  74 

Denominate  Numbers  by  Aliquot  Parts 77 

Graphs 79 

Miscellaneous  Problems 83 

The  Equation 88 

Mensuration • 92 

Practical  Measurements 100 

Special  Methods 106 

Differences  in  Time 106 

Approximations  used  in  Business 107 

Application  of  Practical  Measurements  to  Manual  Training     .  107 

Miscellaneous  Problems 109 

5 


6  '      .         .'.*;•'   CONTENTS 

.•  ,        ,           ',       '        '.  '•    •         •        -             •  PACK 

PERCENTAGfe*        .':•':           :• 117 

Gain  and  Loss 120 

Commercial  Discount 123 

Marking  Goods 128 

Wholesale  and  Retail  Profits 130 

Commission 133 

Miscellaneous  Problems 137 

Interest 144 

Common  Interest 144 

Exact  Interest 151 

Compound  Interest 153 

Sinking  Funds 155 

Banks  and  Banking 157 

Bank  Discount 164 

Present  Worth  and  True  Discount 168 

Partial  Payments 169 

Miscellaneous  Problems 172 

Taxes 180 

Apportionment  of  Taxes 181 

Indirect  Taxes 183 

Insurance 185 

Fire  Insurance 185 

Life  Insurance 189 

Stocks  and  Bonds 192 

Exchange 201 

Domestic  Exchange     .         .        . 202 

Foreign  Exchange 209 

Partnership 213 

Railroad  Rates 215 

Parcel  Post 219 

Miscellaneous  Problems 221 

Review  Problems 227 

Appendix 237 

The  Metric  System 237 

Values  of  Foreign  Coins 241 

Square  Root 242 


BUSINESS  ARITHMETIC 


ADDITION 

1.  Two  things  are  important  in  addition  :  first,  the  figures 
must  be  plain;  second,  they  must  be  arranged  in  straight 
columns  or  rows.  Carelessness  regarding  these  two  details 
is  the  cause  of  many  mistakes. 

Dictation  Work.  Write  the  following  exercises  from 
dictation,  making  the  figures  plain  and  arranging  them  in 
straight  rows  and  columns,  as  for  addition  : 

320615  487931 

826704  593180 

114329  607852 

275016.  738548 

2.  The  basis  of  rapid  addition  is  the  "grouping"  of  figures. 
By  practice  the  eye  can  be  trained  to  group  or  combine  two, 
three,  or  four  figures  into  sums  which  are  recognized  at  sight, 
just  as  we  recognize  words  at  a  glance  without  spelling  out 
the  letters. 

3.  Two-figure  combinations.  The  following  drill,  exercises 
1  to  5,  contains  all  the  possible  groups  or  combinations  of  two 
figures  each  except  1  and.O,  1  and  1.  In  adding  them,  think 
results^  not  separate  numbers.  Thus  (first  columns),  think 
9,  11,  7,  4,  10 ;  not  1  and  8  are  9,  7  and  4  are  11,  etc. 

Give  results  from  left  to  right ;  from  right  to  left ;  from 
top  to  bottom;  from  bottom  to  top;  at  random. 

7 


8  ADDITION 


r.iess.  (  I 

5'   3     3     6     7 


Drill  on  these  until  all  the  results  can  be  read  in  one 
minute  or.less. 

1.  17 '946384^  5  4 
899362884  9  275945 

2.  793129142^7  5^  8  7  53 
418612443  9687753 


:3 

2  6  5  7 

.......  5   ? 

17^84254^ 


3.  31664629  1^6118347 
4282657  58135_9j.92 

4.  2887372915226284 
23637866  7  48  5  3947 


5.  17^84254^5683559 

4.  Add  the  results  of  the  successive  groups  in  rows  1 
and  2;  thus,  9,  20;  16,  26,  etc.  Add  the  results  of  rows  2 
and  3  ;  of  rows  3  and  4 ;  and  of  rows  4  and  5. 

5.  Add  the  results  of  rows  1,  2,  and  3 ;  of  rows  1,  2,  3, 
and  4  ;  of  all  five  rows. 

6.  In  adding,  look  for  those  combinations  whose  sum  is 
10 ;  they  are  easily  recognized  and  added. 

Drill  on  the  following  until  all  the  results  can  be  read  in 
40  seconds  or  less: 

1.  7  16852943 
3  9.  4258167 
£^^^^3^5^ 

2.  14  8"  9  3  6  52  7 
677490317 
962174583 


ADDITION 

9 

3.     3 

1 

5. 

2 

6 

9 

8 

4 

7 

4 

7 

8 

9 

3 

5 

1 

2 

6 

6 

3 

2 

1 

7 

5 

9 

■     8 

4 

4.    7 

2 

9 

5 

2 

5 

4 

2 

1 

3 

6 

9 

3 

7 

1 

3 

1 

6 

4 

8 

1 

4. 

1 

5 

2 

4 

4 

1 

1 

0 

& 

3 

1 

8 

9 

5 

5.     2 

6 

5 

6 

3 

8- 

7 

4 

3 

5 

1 

3 

7 

8 

2; 

9 

7 

2 

8 

.7 

7 

1 

5 

9.' 

1 

6 

9 

a 

4 

8 

9 

5 

8 

5 

3 

7 

7.  Drill  on  the  following  groups,  using  two- figure  com- 
binations and  combinations  of  10 ;  the  60  combinations 
should  be  read  in  one  and  one  half  minutes  or  less. 

1.  179463849589642 
463869  5  66879568 
394778558756^79 

2.  788667  5  22678676 
446647723  2  11476 
241446387221245 


3.  978853173935235 

824798328788784 
2225692  5  2447166 


4.  129822738879933 
499884869565643 
699464523482179 


10  ADDITION 

8.  Add  the  groups  in  rows  1  and  2,  as  suggested  in  §  4 ; 
in  rows  1,  2,  and  3 ;  in  rows  1,  2,  3,  and  4. 

9.  Pick  out,  as  indicated  in  the  first  column,  the  combina- 
tions of  10  in  columns  2-10: 

1.  2.  3.         4.  5.  6.  7.  8.  9.         10. 

7 


3 

4  27         795825         2 

91  135687628 


1)         7        5        2        5        2        5        7        8        7 
51         6        4        7        4        9        3883 


5  1  4         1         6         14         70         4         9 

6  85577  2115 
81  3  4  6  2  4  85  6  4 
2J  75482  6576 
61  3  6  5  116  9  15 
4]  8  3  2  2  3  8  8  9  8 
9  978785928 


10. 

Add: 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

8 

4 

3 

5 

9 

2 

6 

1 

7 

5 

2 

3 

7 

4 

4 

7 

2 

2 

6 

8 

0 

8 

2 

5 

0 

8 

4 

8 

3 

5 

7 

6 

8 

3 

1 

0 

5 

9 

5 

1 

3 

2 

3 

3 

6 

3 

5 

3 

4 

2 

4 

7 

9 

2 

3 

4 

8 

6 

5 

9 

6 

9 

6 

1 

5 

6 

2 

7 

4 

2 

8 

2 

1 

8 

7 

5 

9 

4 

5 

7 

8 

8 

3 

5 

6 

5 

4 

5 

6 

2 

7 

8 

7 

5. 

6 

4 

7 

6 

6 

5 

1 

3 

4 

3 

8 

1 

7 

6 

6 

9 

ADDITION  11 

11.    Read  the  results  in  the  following.     Watch  for  two- 
figure  combinations  and  for  combinations  of  10. 


1.    7 

2 

3 

6 

2 

5 

6 

4 

9 

8 

3 

7 

4 

6 

9 

8 

8 

7 

3 

7 

8 

8 

4 

2 

3 

4 

1 

9 

0 

3 

1 

1 

1 

0 

1 

0 

7 

3 

4 

4 

6 

4 

3 

5 

4 

3 

2 

8 

6 

8 

2.    5 

8 

6 

2 

5 

1 

7 

6 

6 

2 

6 

2 

2 

8 

9 

8 

3 

5 

3 

3 

2 

2 

3 

9 

8 

4 

7 

7 

0 

9 

9 

2 

9 

4 

3 

1 

5 

•  7 

1 

4 

2 

4 

3 

9 

2 

9 

9 

9 

4 

8 

3.    9 

9 

8 

3 

4 

5 

9 

6 

8 

7 

9 

8 

6 

7 

0 

2 

8 

8 

5 

9 

6 

7 

4 

4 

4 

2 

3 

0 

2 

6 

8 

2 

8 

8 

8 

9 

3 

7 

7 

5 

1 

7 

6 

1 

2 

6 

9 

3 

8 

8 

4.     1 

4 

6 

7 

5 

2 

3 

4 

7 

8 

0 

3 

2 

5 

5 

8 

7 

9 

1 

6 

2 

8 

8 

4 

9 

8 

5 

8 

3 

5 

0 

9 

8 

2 

3 

2 

9 

3 

1 

7 

8 

3 

8 

9 

8 

4 

3 

7 

1 

4 

5.     1 

8 

4 

7 

6 

2 

3 

9 

5 

^ 

4 

1 

8 

0 

9 

2 

1 

3 

9 

9 

2 

2 

6 

6 

8 

9 

6 

3 

6- 

4 

7 

6 

8 

3 

1 

6 

7- 

6 

8 

8 

8 

7 

6 

8. 

9 

5 

8 

2 

7 

2 

The  above  results  should  be  read  in  two  minutes  or  less. 


12  ADDITION 

12.  Checking  is  any  means  of  proving  the  accuracy  of  the 
work.  If  the  addition  has  been  made  downward,  check 
by  adding  upward  ;  this  is  the  best  means  of  checking,  and 
usually  locates  any  error. 

13.  Many  accountants  use  the  following  method  in  check- 
ing results  : 

7237 

The  sum  of  the  units'  column  is  21  units 

The  sum  of  the  tens'  column  is  24     tens 

The  sum  of  the  hundreds'  column  is  28       hundreds 

The  sum  of  the  thousands'  column  is  20         thousands 

1875  23061  {check) 
23061 


5641 

2872 
5436 


14.   The  method  of  checking  known  as  casting  out  nines 

is  sometimes  used. 


i^rA    o  Add  the  digits  in  each  addend,  dropping  the  nines  as  you 

do  so.    Drop  4  +  5  (9),  and  put  down  the  2.    In  the  second 
^^  ^     row  drop  8  +  1,  and  put  down  0  (no  remainder).    In  the  third 
885   3     row,  5  +  8  =  13,  drop  9,  leaving  4 ;  4  +  8  =  12  =  one  9  and  3 
763   7     over.    The  remainder  in  the  fourth  row  is  7,  and  in  the  fifth,  0. 
(575   Q     Adding  the  several  remainders,  we  get  12  (one  9  and  3  over)  ; 
2(jgc    Q     dropping  the  9's  in  the  result  gives  a  remainder  3.    The  addi- 
tion, therefore,  is  probably  correct. 

15.  In  writing  or  copying  numbers,  any  error  caused  by 
transposing  the  figures  of  a  number  is  divisible  by  9  ;  mis- 
takes may  often  be  located  in  this  way.  Thus  an  error  of  #  90 
might  have  been  caused  by  writing  |328  instead  of  #238  or 
vice  versa ;  writing  54  instead  of  45  gives  an  error  of  9,  etc. 


WRITTEN   WORK 

16.  Add  the  following  problems  by  combinations  of  two 
figures  ;  remember  always  to  look  for  sums  which  equal  10  ; 
check  results  by  any  method. 


ADDITION 

13 

1.      2. 

3. 

4. 

5. 

6. 

7. 

538   7622 

68498 

243967 

942268   98254 

820328 

694   8431 

71527 

885354 

239592   94893 

538964 

287   6691 

42936 

476932 

873240   67868 

932599 

436   4424 

22679 

732369 

952823   39675 

813836 

393   3739 

39338 

529437 

842637   93464 

376207 

962   7385 

78075 

952546 

749894   74649 

933963 

452   9461 

68627 

689475 

376846   38473 

670244 

836    318 

24496 

396823 

367298   72967 

592683 

^■i'{ 

8. 

9. 

10. 

11. 

12. 

2468998 

2369857 

539863 

6892576 

6864939682 

810773 

784972 

284006 

380919 

926784629 

3106064 

38648 

186 

6808 

16930179 

2958 

414973 

8675 

8329727 

8202904625 

16476 

8754 

934 

986235 

623968234 

286972 

43692 

681309 

6809763 

9813952975 

3296498 

57373 

372691 

4682792 

9239392839 

968634 

865885 

458 

8257613 

2895.12954 

6976 

16862 

914 

398458 

6396832689 

4163068 

6197837 

682789 

2918975 

2139323692 

13. 

14. 

15. 

16. 

62534785 

1211678.92 

4519904 

325 

42768 

4376.53 

80022 

279002 

3426487 

52678.21 

3428 

369001 

546891 

5S6M 

319900 

32673 

63916294 

23891.78 

538 

299751 

"-^354689 

996784.46 

7723901 

6867 

552679 

8228.77 

47892 

2871909 

64738923 

48935.25 

72804 

4572 

634258 

243.85 

992367 

70003 

7354629 

25364.48 

734 

247808 

300030 

114.15 

63425 

375803 

34253645 

65.65 

6354745 

8675391 

14 

ADDITION 

17. 

18. 

19. 

20. 

258014675 

334990800 

2508146 

4466820 

39820017 

100336472 

567 

30004 

287941 

5541763 

268749 

638914410 

47190285 

639014725 

75271 

36819304 

832091748 

472459016 

33728451 

591309247 

47251635 

61538697 

163089 

1648732 

845361924 

46573100 

2537481 

90057338 

635127400 

361022855 

46275541 

900036211 

714257892 

5326178 

243885 

11922347 

364511 

56640 

273101 

4457 

38165243 

88129934 

7142386 

553896452 

3732450 

632871 

79573 

2004893 

992345515 

3745106 

26374810 

7342888 

5645 

40009786 

1118885 

375642102 

4994494 

61195 

836 

20 

437611 

1589298 

463702 

4582901 

634459011 

2266839 

8629815 

33561 

900026733 

63825637 

41432678 

71280090 

To  THE  Teacher.  Inability  to  write  or  copy  numbers  accurately  is 
the  cause  of  frequent  mistakes.  Dictate  the  above  numbers,  and  then 
cause  the  woik  to  be  checked  for  accuracy  and  legibility.  Make  frequent 
use  of  dictation  exercises  of  this  kind. 

Note.  In  offices  the  expression  to  "  foot-up,"  meaning  to  "  add,"  is 
frequently  heard  ;  the  sum  is  called  the  "  footing." 

17.  Horizontal  addition.  In  invoices  and  in  arrangements 
of  numbers  in  tabular  form,  it  is  sometimes  necessary  to 
add  numbers  horizontally.  Care  should  be  taken  to  combine 
figures  of  the  same  order :  units  with  units,  tens  with  tens, 
etc.  Do  not  attempt  to  add  hoj'izontally  if  the  numbers  are 
very  long  ;  place  a  dot  over  each  figure  as  it  is  added. 

.1.  Find  (a)  the  total  native  parentage,  (5)  the  total 
foreign  or  mixed  parentage,   (c)  the  foreign  whites,  {d)  the 


ADDITION 


15 


total  negro  population,  (e}  the  total  population  of  each  city. 
Check  your  work. 


1910  Census  for  Cities  of  Ohio 

City 

Native 
Parentage 

Foreign 
OR  Mixed 
Parentage 

Foreign 
Whites 

Negro 
Population 

Total 

Akron     . 

Canton   . 

Cincinnati 

Cleveland 

Columbus 

Dayton  . 

Hamilton 

Lima 

Lorain    . 

Newark  . 

Springfield 

Toledo    .     . 

Youngstown 

Zanesville 

37793 

29470 

154937 

132314 

116486 

72301 

21866 

23465 

8455 

19090 

30577 

75114 

25595 

20885 

17370 

11798 

132190 

223908 

35578 

25559 

9371 

4445 

9112 

3914 

8243 

59383 

26654 

4145 

13241 
6848 

56792 
195703 

16285 

13847 
3309 
1614 

10929 
1602 
3156 

32037 

24840 
1602 

657 

291 

19639 

8448 

12739 

4842 

725 

978 

375 

1384 

4933 

1877 

1936 

1384 

Total  .     . 

2.  Complete  the  following  sales  sheet.  Add  by  columns 
and  by  rows,  and  check  the  work  by  adding  the  vertical  and 
horizontal  totals  and  comparing  the  two  amounts. 

Summary  for  Week  Ending  July  25 


Caki'ets 

Furniture 

Stoves 

Books 

Dishes 

Total 

Mon. 

$2436.15 

$8654.72 

$  237.58 

$  972.15 

$  238.17 

Tues. 

754.13 

2364.58 

2364.25 

764.73 

1324.82 

Wed. 

1356.64 

1655.18 

1293.70 

1215.14 

2652.73 

Thurs. 

592.35 

2736.63 

75. 

836.58 

1736. 

Fri. 

2317.59 

9872.50 

4378.56 

72. 

3642.75 

Sat. 

1654. 

6375.25 

1654.19 

2315.04 

1568.09 

Total 

16 


ADDITION 


3.  The  number  of  pupils  in  school  was  as  follows,  as 
indicated  by  buildings  and  by  grades.  How  many  were 
there  in  each  grade  ?   in  each  building  ?    Check  your  work. 


GUADE 

Washing- 
ton 

Lincoln 

Jefferson 

Fbanklin 

NOETH 

Central 

Total 

1 

108 

62 

45 

43 

94 

2 

103 

50 

42 

39 

87 

3 

95 

48 

37 

39 

73 

4 

92 

43 

33 

30 

66 

6 

83 

41 

29 

28 

51 

6 

72 

37 

26 

25 

47 

7 

55 

31 

19 

20 

40 

8 

41 

28 

17 

20 

36 

H.  S. 

•834 

Total.  . 

• 

SUBTRACTION 

18.  The  most  rapid  method  in  subtraction  is  illustrated 
as  follows:  suppose  you  wish  to  subtract  8615  from  9521. 

9521  ^^y  *°  yourself:  5  and  6  (put  down  the  6)  are  11,  carry  1; 

on-,  r  2  (1  +  1  carried)  and  0  (put  down  the  0)  are  2 ;  6  and  9  (put 

^      '  down  the  9)  are  15 ;  4  (3+1  carried)  and  5  are  9.     Put  down 

S906  the  5. 

In  other  words  you  are  to  find  that  number  which  added  to 
3615  will  give  9521. 

19.  Ease  and  rapidity  in  subtraction  will  come  with  prac- 
tice. Drill  on  the  following,  reading  the  differences  at  sight. 
The  eiglity  results  should  be  read  in  a  minute  and  a  half. 

1.  84596989738974798 
23154744331360532 


2. 

11 

16 

13 

13 

10 

11 

14 

15 

17 

14 

12 

13 

19 

5 

^ 

7 

5 

J 

_J 

_8 

_9 

8 

3 

_9 

_8 

_3 

3. 

15 

19 

16 

14 

18 

17 

13 

18 

14 

11 

19 

15 

16 

^ 

7 

11 

8 

12 

_5 

11 

_6 

J 

_4 

13 

_6 

13 

4. 

21 

14 

19 

23 

22 

51 

20 

24 

21 

20 

22 

26 

21 

15 

4 

12 

15 

17 

13 

14 

19 

18 

18 

13 

15 

17 

5. 

38 

35 

41 

37 

25 

42 

51 

47 

81 

62 

93 

46 

87 

29 

26 

38 

18 

19 

26 

17 

39 

79 

45 

47 

32 

16 

6. 

175 

205  193 

600 

750 

215  7C 

)    195  219 

351 

514 

68 

42  151 

480 

514 

155  57 

'   89  198 

248 

328 

BUS,  ARITH. 2  17 


18  SUBTRACTION 

20.  Checking.  The  best  way  to  check  subtraction  is  to 
add  (upward)  the  remainder  to  the  subtrahend,  checking 
tlie  result  by  the  figures  in  the  minuend  as  you  do  so. 
Thus  in  §  18,  6  +  5  =  11  (check  the  1),  0  +  1  +  1  =  2  (check), 
9  +  6=  15  (check),  5  +  1+3  =  9. 

21.  A  parenthesis,  (  ),  signifies  that  all  quantities  within 
it  are  to  be  considered  together.  A  vinculum  —  written  over 
the  numbers  has  the  same  effect.  For  example,  17  —  (6  +  4), 
or  17  —  6  +  4,  means  that  the  sum  of  6  and  4  is  to  be  sub- 
tracted from  17. 

22.  In  making  change,  add  to  the  amount  of  the  purchase 
tlie  amount  necessary  to  equal  the  coin  or  bill  tendered  in 
payment. 

1.  If  a  man  buys  goods  amounting  to  $2.53,  and  tenders 
a  twenty-dollar  bill,  how  will  the  cashier  count  out  the 
change  ? 

The  cashier  picks  out,  first  2^,  then  2  dime.s,  then  a  quarter,  then 
a  |2  bill,  then  a  !$5  bill,  then  a  $10  bill  (not  two  5's),  making  $20. 
The  change  is  counted  out  piece  by  piece,  thus:  $2.53,  $2.54,  $2.55, 
$2.65,  $  2.75,  $  3,  $  5,  $  10,  $  20. 

Count  out  the  change  in  the  following  : 

2.  15  -*2.15 

3.  110 -$1.73 

4.  no-  16.13 

5.  120 -$11.42 

Cost  of  the  items  purchased 

10.  1.25,      $8.25,     $1.25 

11.  $.14,       $1.52,     $2.11 

12.  $21.25,  $17.82,  $16.54 

23.  To  find  the  arithmetical  complement  of  a  number,  sub- 
tract it  from  one  unit  of  the  next  higher  order.     Thus,  the 


6. 

$2 -$.72 

7. 

$1-$.14 

8. 

$.75-  $.52 

9. 

$.50 -$.11 

Amount  tendered 

$10 

$5 

$100 

SUBTRACTION 


<3 


complement  of  8  is  2  (10  —  8)  ;  the  complement  of  89  is  11 
(100  -  89). 

Arithmetical  complements  are  useful  in  getting  the  result 
in  any  problem  which  requires  that  one  number  be  subtracted 
from  the  sum  of  other  numbers. 

1.  Find  the  result  of  764  minus  121  plus  263. 

Arrange   as  for   addition,    prefixing   a   minus  sign  to  the 
'  ^^      quantity  to  be  subtracted.     Add,  using  the  complement  of  the 

—  121      minus  figure  in  each  column;  thus,  4  +  9   (the  complement  of 
263       1)  +  3  =  16 ;  write  6,  rejecting  one  10,  there  being  one  minus 

'      QQg      number.     Continuing,  6  +  8  (complement)  +  6  =  20  ;  write  0, 
reject  10,  carry  1.     8  +  9  +  2  =  19;  write  9. 

(a)  When  the  sum  in  any  column,  including  the  comple- 
ment, is  less  than  10,  put  down  the  entire  sum,  and  add  1 
to  the  minus  figure  in  the  next  column  before  finding  its 
complement. 

(5)  The  complement  of  0  is  10. 

2.  Find  the  result  of  1360.40  minus  117.08  plus  f  114.25. 

0  +  2  (complement  of  8)  +  5  =  7  ;  write  7.     Since  10  can- 
^t'ooU.'lU      jjQ^  ]jQ  subtracted,  add  1  to  0,  the  minus  number  in  the  next 

—  17.08       column,  before  finding  its  complement.     4  +  9  (complement 
114.25      of  0  +  1)  +  2  =  15 ;  reject  10;  write  5.     0  +  3  (complement 

$457  57      ^^  7)  +  4  =  7.     10   cannot  be  subtracted.     6  +  8    (comple- 
ment  of   1  +  1)  +  1  =  15;    write    5.      3+1  =  4;    write    4. 
There  being  no  minus  figure  in  this  column,  no  10  is  rejected. 

24.  Solve  the  following  by  complementary  addition. 


1. 

2. 

3. 

4. 

5. 

257 

118.54 

$854.25 

328 

$2116.45 

196 

7.52 

-  75.93 

-7 

-.58 

-318 

54.85 

156.55 

421 

36.71 

254 

-10.50 

129.62 

36 

411.95 

716 

19.87 

73.54 

880 

3246.78 

119 

5.52 

254.76 

706 

21.16 

20 


SUBTRACTION 


25.  Balancing  accounts.  The  following  is  taken  from  a 
bank  ledger.  It  shows  (1)  each  person's  balance  at  the 
beginning  of  the  day,  (2)  the  amount  drawn  out  by  check, 
(3)  the  amount  deposited. 

1.    By  horizontal  complementary  addition  determine  each 

person's  balance  at  the  close  of  the  day.     Check  by  vertical 

addition. 

Depositor's  Ledger 


Names 

Balance 

Checks 

Deposits 

Balanok 

Mr.  A 
Mr.  B 
Mr.  C 
Mr.  D 
Mr.  E 

' 

li 

H 
If 

)7 
)8 
)0 
)6 
)4 

24 

25 
18 

2i 
1^ 

1( 

JO 
}4 
10 

L2 
)0 

15 
25 

] 

] 

] 

56 
29 
10 

148 
M8 

28 

57 
22 

Total 

2.  When  the  debit  and  credit  items  of  an  account  are 
given,  this  is  a  convenient  method  of  determining  the  balance. 
This  is  important  because  of  its  wide  use  in  bookkeeping. 

The  debit  side  of  the  account 
is  obviously  the  larger ;  foot  this 
account  and  write  in  the  footing, 
.16698.04,  for  both  debit  and 
credit  columns.  Add  the  credit 
side  thus  :2  +  5+l  +  2  +  (4)  = 
14;  put  down  the  (4)  and 
carry  1.  Continuing,  1  (carried) 
+  7  +  7  +  5  +  9  +  (1)  =  30,  etc. 
Check  by  adding  the  credit  col- 
umn including  the  balance. 

Solve  by  the  balancing  account  method  : 

3.  Balance  in  bank  June  1,  1914,  $450.  Checks  from 
June  1st  to  June  30th,  $25.35,  $124.00,  $17.62,  $18.42, 
$42.54.     What  is  the  balance  July  1st? 


Cash 

Dr. 

Cr. 

2r 

( 

li 

2] 

)86 
554 
}64 

142 

J98 

24 

25 
82 
73 

< 

2t 
15 
1{ 

168 
)68 
J56 
254 
)49 

72 
75 
51 
92 
14    Bal. 

6( 

04 

6( 

598 

04 

SUBTRACTION  21 

4.  A  man  bought  a  farm  for  #8260.  He  built  a  house 
on  it  at  a  cost  of  $1850  and  fences  cost  -1240.  What  was 
his  gain  if  he  sold  it  for  111000? 

5.  A  man's  salary  is  1 1500  pe.  ).iiu.  it  he  requires  for 
rent  1 300,  for  personal  expenses  |:!*r'-^>8,  and  for  household 
expenses  1816.27,  what  amount^ wIIlc  !iave  left  at  the  end 
of  the  year  ? 

6.  In  an  election  the  votes  for  the  candidates  A  and  B 
in  five  wards  were  as  follows : 


ABD 

A 

B 

1 

1261 

832 

2 

793 

1116 

3 

1030 

755 

4 

1349 

624 

5 

998 

977 

majority 

Which  candidate  has  a  majority?  How  large  is  the 
majority? 

7.  Arrange  in  proper  form  and  find  the  balance  for  July 
1st.  Deposits:  Jan.  1,  i300;  Feb.  3,  1250;  March  2, 
1150;  June  28,  1250.  Checks:  Jan.  16, -f  125. 30;  Feb.  7, 
175.20;  June  18,  195.18. 

8.  A  cash  register  showed  the  following  record  of  the 
daily  sales  of  two  clerks.     Which  sold  the  more  goods,  and 

B 

$  27.61 
126.13 

81.35 
134.25 

84.16 
194.68 


how  much? 

j^ 

Monday 

.     $  43.85 

Tuesday     .     . 

78.94 

Wednesday     . 

.     .         90.09 

Thursday  . 

.     .       148.72 

Friday  .     .     . 

.     .       110.27 

Saturday    .     . 

.     .       213.50 

22 


SUBTRACTION 


Determine  the  balance  in  the  following :  — 


9. 

10. 

LI. 

Db. 

Cr. 

De. 

Or. 

Dr. 

Or. 

$  236.97 

14657.81 

$  421.07 

$3118.72 

$200. 

$5000. 

2436.18 

753.34 

1872.56 

550. 

231.46 

428.70 

1846.90 

624.83 

396.54 

27.81 

61.69 

1000. 

115.00 

524.65 

2148.19 

642.90 

568.89 

246.66 

198.75 

312.40 

Bal. 

940.07 

168.17 

Bat.. 

301.01 

1587.75 

I 

Bal. 


12. 


THE  CITY  NATIONAL  BANK 


In  Account  wi 

^ 

U 

^ 

0 

-. 

>.^^. 

- 

Date 

Withd 

rawn 

Deposited 

Balance 

(L^. 

/ 

£:^A4L 

■^"   ^ 

f 
tr. 

■L 

?.,1 

^0  7  S- 

{T^ 

7. 

/ 

,? 

7 

s 

. 

o 

J 

/  ^ 

So  o 

<r 

7 

5 

0 

o 

o 

^ 

7 

1 

f 

(o 

0. 

7 

7  5 

OiS 

/o 

3 

2 

^ 

S 

f 

/2 

7 

S30 

20 

37 

%^0 

^7 

2 

7 

2 

^ 

Z 

2S 

^7 

S  00 

3 

f 

o 

0 

o 

19 

.!. 

o 

0 

Write  the  above  from  dictation  and  fill  in  the  balance 
column.  Test  the  balance  for  Jan.  30th  by  the  method  in 
exercise  2. 


MULTIPLICATION 

26.  Good  work  in  multiplication  depends  upon  a  knowl- 
edge of  the  multiplication  tables.  Products  of  numbers  up 
to  15  ought  to  be  recognized  at  sight. 

Thus  9x6,  or  6x9,  should  suggest  54  just  as  readily  as 
9  +  6  suggests  15. 

27.  Drill  on  the  following  table  until  products  can  be  read 
without  hesitation. 

As  in  addition,  think  results. 


1 

2 

2 
4 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

1 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

2 

3 

6 

9 

12 

15 

18 

21 

24 

27 

30 

33 

36 

39 

42 

45 

3 

4 

8 

12 

16 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

4 

6 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55 

60 

65 

70 

75 

5 

6 

12 

18 

24 

30 

36 

42 

48 

64 

6Q 

m 

72 

78 

81 

90 

6 

7 

14 

21 

28 

35 

42 

49 

56 

63 

70 

77 

84 

91 

98 

105 

7 

8 
9 

IH 
18 

24 

32 

40 

48 

56 

64 

72 

80 

88 

96 

104 

112 

120 

8 

27 

36 

45 

54 

63 

72. 

81 

90 

90 

108 

117 

126 

136 

9 

10 
11 

20 
22 

30 
33 

40 

50 

60 

70 

80 

90 

100 

110 

120 

130 

140 

150 

10 

44 

55 

66 

77 

88 

99 

110 

121 

132 

143 

154 

165 

11 

12 
18 
14 

24 

26 

28 

36 

48 

60 

72 

84 

96 

108 

120 

132 

144 

156 

168 

180 

12 

39 
42 

52 

50 

65 

78 

91 

104 

117 

130 

143 

156 

169 

182 

196 

13 

70 

84 

98 

112 

126 

140 

154 

168 

182 

196 

210 

14 

15 

30 

45 

60 

75 

90 

105 

120 

135 

150 

165 

180 

195 

210 

225 

15 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

23 


24  MULTIPLICATION 

2a  Multiply  257  by  28. 

Zoi  The  product  56  should  be  suggested  without  thinking  "8x7 

28  is  56  " ;  write  the  6.     Next,  think  "  forty  (8  x  5)  five  "  (carried)  ; 

2056  write  the  5.     Likewise,  the  next  result  thought  should  be  20. 

CI  4  Complete  the  multiplication  in  this  way.     In  adding  the  partial 

rr-,Qr»  products,  apply  methods  for  rapid  addition. 


Multiply 
1. 

2. 

3. 

4. 

5. 

258 

372 

156 

276 

578 

37 

83 

17 

46 

152 

6. 

7. 

8. 

9. 

10. 

325 

768 

-698 

896 

1258 

247 

359 

476 

754 

3267 

To  THE  Teacher.  Until  the  correct  method  is  learned,  require  all 
work  to  be  done  orally. 

29.  Checking.  The  best  method  of  proving  the  result 
correct  is  to  interchange  the  factors.  Thus,  in  example 
9  above,  check  the  product  of  896  x  754  by  multiplying 
754  X  896. 

Multiplication  may  be  checked  also  by  casting  out  the 
nines.     The  following  example  will  illustrate  the  method. 

536  5 

I Y3  2  ^^®*  ^^^  ^^®  nines  in  the  sum  of  the  digits  of  each  factor ; 

"YTTTT^  ~  find  the  product  of  the  remainders  (5  and  2)  and  cast  out 

^ the  nine;  the  remainder  CI)  should  be  the  same  as  that 

found  in  casting  out  the  nines  in  the  sum  of  the  digits  in 

536  ^  the  result. 

92728  1 

Multiply  and  check  : 

1.   4672  2.    5736  3.    8245  4.    1213 

801  954  3107  1012 


MULTIPLICATION  25 

RAPID    METHODS   IN   MULTIPLICATION 

30.  To  multiply  by  lo,  100,  1000,  etc.  Annex  as  many 
ciphers  to  the  multiplicand  as  there  are  ciphers  in  the 
multiplier. 

To  multiply  by  20,  30,  600,  etc.     Multiply  first  by  the  2,  3, 
etc.,  and  then  annex  the  necessary  ciphers. 
Give  results  orally : 

1.  24  X  60  4.    350  X  100  7.    724  x  300 

2.  214  X  200  5.    706  x  20  8.    964  x  20 

3.  320  X  30  6.    826  x  60  9.    830  x  70 

31.  Complements  (§  23)  may  be  used  in  multiplying  when 
the  figures  of  the  factors  are  between  80  and  100. 

Multiply  97  by  95. 

97      3  (comp.)  Write  15,  the  product  of  the  complements  as 

^5  5  Tcomn  ^  illustrated;  subtract  either  complement  from  the 
QtyTF  other  factor  (05  —  3  or  97  —  5)  and  prefix  the  re- 

mainder to  the  15. 

Note.  If  the  product  of  the  complements  is  one  figure,  prefix  0;  if 
more  than  two  figures,  set  dawn  the  last  two  figures  and  carry  the  other 
to  the  next  part  of  the  product. 

Write  the  products  of  tlTe  following: 
1.  2.  3.  4.  5.  6. 

93        98        91         95        86         85 

92         91         93         8J)     '   96         95        _        _        _ 

32.  To  multiply  by  ii. 
Multiply  23724  by  11. 

Write  down  the  right-hand  figure  (4)  ;  write,  in  order, 

23724        ^i^g  g^^„^  Qf  ^jjg  Ig^  ^^^  2d  figures  (4  -|-  2),  the  sura  of  the 

11         2d  and  3d  (2  -f  7),  the  sum  of  the  3d  and  4th  (7  -f  3),  the 


7. 

8. 

9. 

84 

98 

84 

98 

97 

86 

260964         sum  of  the  4th  and  5th  (3  +  2)  +  1  (carried)  ;  write  2,  the 
left-hand  figure. 
NoTEe      To  multiply  a  number  of  two  figures  by  11,  write  the  sum  of 
the  two  figures  between  them ;  thus,  35  x  11  =  385. 


26 


MULTIPLICATION 


Multiply  : 

1.  43  by  11. 

2.  1572645  by  11. 

3.  82354  by  11. 

4.  9872365  by  11. 

5.  1872596  by  11. 


6.  3824  by  11. 

7.  168549  by  11. 

8.  873180  by  11. 

9.  9072  by  11. 
10.  431807  by  11. 


33.   To  multiply  by  a  number,  one  part  of  which  is  a  multiple 
of  another  part. 

Multiply  265  by  357. 

265 


357 


1855 
9275 


The  product  of  265  x  7  is  1855 ;  35  is  5  times  7,  hence  mul- 
tiply 1855  by  5  and  set  down  the  first  figure  under  the  5  of  the 
35. 


94605 

Multiply  285  by  728. 

285  It  does  not  matter  which  number  in  the  multiplier  is 

Y28  fii'st  used,  if  the  product  is  written  under  the  number  by 
which  we  multiply..  Therefore,  multiply  first  by  7,  setting 
down  1995  so  that  the  first  figure  (5)  comes  under  the  mul- 
tiplier (7)  ;  multiply  that  result  (1905)  by  4  (28  =.4x7), 
writing  7980  so  that  the  0  is  under  the  8  of  28. 

Note.     In  all  multiplication  work  be  careful  to  keep  all  columns 
straight,  especially  when  there  are  a  number  of  partial  products. 

Multiply  :  (check) 


1995 

7980 
207480 


1.  9512x279 

2.  8326  X  327 

3.  16547  X  426 

4.  72543  X  6611 

5.  4872  X  321 

6.  5419  X  355 


7.-  342468  X  24366 

8.  62857  X  105357 

9.  165478  X  9254 

10.  625487  X  72135 

11.  780855  X  2408 

12.  96382  X  3612 


MULTIPLICATION 


27 


EXERCISES 


1. 

384965 
257 

2. 

84563 
355 

3. 

98376 
14503 

4. 

58764 
4267 

5. 

78456 
99011 

6. 

31528 
3024 

7. 

72349 

1608 

8. 

398107 
12372 

9. 

578655 
4657 

10. 

1394764 

10958 

11. 

2358762 
428363 

12. 

7938767 
4305008 

13. 

72859001 
3800 

14. 

54009768 
948358 

15. 

87210324 
7864573 

16.  A  factory  employs  2317  men  at  an  average  wage  of 
12.50  per  day.  If  there  are  26  working  days  in  the  month 
of  July,  what  amount  will  be  paid  out  in  wages  ? 

17.  The  average  taken  in  by  a  street-car  conductor  per 
day  is  f  53.75.  What  amount  will  be  taken  in  by  197  con- 
ductors in  31  days  ? 

18.  Multiply  the  sum  of  84354  and  17690  by  the  difPerence 
between  53643  and  11319. 

19.  Following  the  form  in  §  27,  prepare  a  multiplication 
table  of  numbers  from  16  to  25. 

20.  An  automobile  manufacturer  makes  in  one  year  2678 
machines  of  an  average  value  of  il275.  What  is  the  value 
of  his  output  ? 


DIVISION 

RAPID   METHODS   IN   DIVISION 

Note.  Special  methods  depending  on  fractions  will  be  taken  up  after 
that  subject  has  been  presented. 

34.  To  divide  by  lo,  loo,  looo,  etc. 

Beginning  at  the  right-hand  figure  of  the  dividend,  or  at 
the  decimal  point,  point  off  as  many  places  to  the  left  as 
there  are  ciphers  in  the  divisor. 

35.  To  divide  by  30,  400,  5000,  and  like  numbers. 

Point  off  the  required  number  of  places,  and  divide  by  the 
left-hand  figure  of  the, divisor. 

Give  results  orally : 

1.  853427  -60  9.  27000   -  3000 

2.  25324    --300  10.  1425     -^600 

3.  742592  --  1000  11.  3961     --  70     • 

4.  365867-200  12.  7204     -90 

5.  158392-400  13.  170693-30 

6.  267840-20  14.  554010-800 

7.  461973-10  15.  913563-100 

8.  817700-2000  16.  150000-30000 

36.  To  divide  by  the  factors  of  a  number. 
Divide  3759  by  21. 

3)3759 

7^)1253  ^^^  factors  of  21   are  3   and  7;   divide  by  short 


179 


division. 


DIVISION 


29 


Divide  24667  by  105. 

3)24667 
5)  8222  +  1 
7)  1644  +  2x3  = 
234  +  6  X  5  X  3  = 


1 

6 
90 
97 


The  factors  of  105  are  3,  5,  and  7. 
Divide  by  these  in  turn,  setting 
down  the  remainder,  if  any.  Multi- 
ply each  remainder  by  all  previous 
divisors,  and  add  these  products  for 
the  final  remainder. 


Note.  If  the  division  is  exact  will  there  be  any  remainder  at  any 
time  during  the  operation  ?    Why  ? 

37.  Checking.  The  best  method  of  clieckiiig  division  is 
to  multiply  the  quotient  by  the  divisor  and  add  the  re- 
mainder ;  the  result  should  equal  the  dividend. 

38.  Division  may  be  checked  by  casting  out  nines. 

The  excess  of  9's  in  the  divisor  is  6 ; 
Divide  24667  by  105.  in  the  quotient  0 ;  in  the  remainder  7. 
(See  §  36.)  6x0  plus  7  equals  7,  the  excess  in  the 

dividend.    The  result  is  probably  correct. 


EXERCISES 

Divide  by  the  factor  method  : 

1.    72348  H- 64 

6. 

82492  -  99 

2.    35678 -V- 84 

7. 

15436  -i-  96 

3.    54792-54 

8. 

62743  - 108 

4.    4594-42 

9. 

879654  ^  72 

5.    41687^56 

10. 

247859  ^  88 

Divide  each  of  the  following  by  10  ;  by  100  ;  by  1000  ;  and 
by  10000 ; 

11.  48000  15.  4900000  19.  20000000  23.  34621 

12.  3650000  16.  28490000  20.  21900000  24.  8540 

13.  50000  17.  5800000  21.  4758  25.  17543- 

14.  850000  18.  85000000  22.  73954  26.  75436907 


30 


DIVISION 


Divide  by  long  division  :   (check) 


27.  749680-768 

28.  793465-^435 

29.  389576^7820 

30.  972683^8726 

31.  698374^5925 


32.  379446-^5428 

33.  940786^5087 

34.  987206 -T- 7408 

35.  849752^42785 

36.  342736-^-34271 


37.    A  state's  fruit  crop  of  168,953,967  bushels  is  valued 
at  1337,907,934.     What  is  the  value  per  bushel? 


38.    A  groc( 

3r  s  sales  for  one 

year  were  as  tollo^ 

ws  : 

January 

.     11154.28 

July  .     .     . 

$  990.17 

February     . 

877.52 

August  .     . 

1098.51 

March     .     . 

.       1036.63 

September  . 

1130.50 

April      .     . 

1124.65 

October 

1187.98 

May  .     .     . 

1206.86 

November   . 

1312 

June  .     .     . 

.       1208.90 

December    . 

1400 

What  were  his  average  sales  per  day,  allowing  26  days  to 
the  month  ? 

MISCELLANEOUS   PROBLEMS 

As  you  solve  each  problem,  compare  the  result  with  the 
statement  of  the  problem  and  decide  whether  it  is  sensible. 

Group  1 

1.  Add  1294.26,  1117.11,  1300,  $52.25,  17.64,  $.18, 
13.17, 11.95,  $219.78,  11340.05,  $8.01,  $27.17. 

2.  Brown  and  Jones's  books  show  the  following  accounts 
receivable  :  $805.74,  $251.06,  $17.85,  $239,  $84.50,  $371.98, 
$726.24,  $73.12,  $304.05,  $420.19,  $35,  $34.21,  $15.10, 
$425.50.     What  amount  is  due  the  firm  ? 

3.  Find  the  totals  in  the  following  table  by  horizontal  and 
by  vertical  addition  ;  check  the  work. 


MISCELLANEOUS 

PROBLEMS 

31 

Acres  Harvested 

Year 

Corn 

Oats 

Wheat 

Potatoes 

TOTAtS 

1909 

3916050 

1787496 

1827932 

212808 

1899 

3826013 

1115149 

3209074 

167590 

1889 

3189553 

1215355 

2269585 

185393 

1879 

3281923 

910388 

2556134 

175487 

Total  .... 

Alternately  add  and  subtract  the  following  : 

4.    3758649 

5.    98725648 

6.    135286.06 

2816754  (add) 

76463580 

26471.75 

1932935  (subtract) 

2990031 

46209.90 

4718264  (add) 

534200 

1000.00 

3758927  (subtract) 

79753546 

12994.37 

2014896  (ad 

d) 

1010357 

1446.46 

7.  A  man  purchases  a  hat  for  f  3,  a  pair  of  gloves  for 
11.50,  a  shirt  for  f  1.15,  four  handkerchiefs  at  2  for  25^, 
6  collars  at  2  for  25^,  and  a  pair  of  shoes  for  $  3.50.  If  he 
tenders  a  twenty-dollar  bill  in  payment,  how  will  the  cashier 
count  out  the  change  ? 

8.  Find    the   result   of    1619.20,    minus   f  24.05,    plus 

1210.86,  plus  J^  744.08. 

9.  Find  the  balance  in  the  following  account  :  debit 
items,  82345.28,  $174.29, 12392.82, 14412.37  ;  credit  items, 
1861.95,  8  340,  $3538.09,  $1746.03. 

10.    Arrange   as  in   problem    12,   page^  22,  and   find   the 


32 


DIVISION 


balance  Jan.  1,  1915.  Deposits.  Jan.  1,  1914,  $500  ;  Mar. 
10,  f  360.25;  June  19,  $195.50.  Checks.  Feb.  18,  $54; 
Mar.  23,  $  27.50  ;  June  15,  $85.10  ;  Nov.  20,  $125. 


Multiply  : 

Group  2 

1. 

3547621 

6408 

2. 

500473 
2463 

3. 

97 
92 

4. 

3740752 
642 

5. 

9364521 
11 

Divide : 

6.  7.  8.  9. 

218568^42     64706-^-434     893458-1724     276938^-2615 

10.    A  planter  raises  1368401  pounds  of  cotton  on  2600 
acres.     What  is  the  average  per  acre  ? 

Group  3 

1.  If  the  remainder  is  430,  the  quotient  1148,  and  the 
dividend  876354,  what  is  the  divisor  ? 

2.  If  75  acres  of  land  produce  3000  bushels  of  corn,  how 
many  bushels  will  140  acres  produce  ? 

3.  A  grain  broker  sells  5  cars  of  corn  of  1000  bushels 
each  at  Qb^  per  bushel.     What  is  the  value  of  the  shipment  ? 

4.  B  buys  chemicals  at  $1.85  per  100  pounds.  What  is 
the  cost  of  a  shipment  of  100  barrels  weighing  378  pounds 
each,  the  weight  of  an  empty  barrel  being  20  pounds  ? 

5.  A  farmer  purchased  a  125-acre  farm  for  $11,200;  he 
sold  50  acres  at  $100  per  acre.  If  he  wishes  to  gain  $1000 
on  the  entire  transaction,  for  how  much  per  acre  must  he 
sell  the  remainder  ? 

6.  What  number  subtracted  227  times  from  826,946  will 
leave  a  remainder  of  212  ? 


MISCELLANEOUS  PROBLEMS  33 

7.  Arrange  as  in  problem  1,  page  20,  and  determine  each 
person's  balance  at  the  close  of  the  day.     Check  your  work. 

On  March  10,  A's  balance  is  $8224.10,  he  deposits  1 213.47, 
and  checks  out  $95.50. 

B's  balance  is  1210,  he  deposits  f  25.75,  and  checks  out 
135.04. 

C's  balance  is  $1000,  he  deposits  $100,  and  checks  out  $25. 

D's  balance  is  $1305.01,  he  deposits  $2700,  and  checks  out 
$1315.82. 

E's  balance  is  $437.98,  he  deposits  $105.17,  and  checks 
out  $50. 

8.  A  salesman  travels  4126  miles  at  an  average  cost 
of  2^^  per  mile  for  railroad  fare.  His  trip  takes  him  41 
days,  during  which  time  he  spends  an  average  of  $4.15 
per  day  for  hotels  and  incidental  expenses.  What  is  the 
cost  of  the  trip  ? 

9.  From  the  following  exports  of  domestic  merchandise, 
find  the  total  number  of  bushels  exported  and  the  total  value 
of  the  exports. 

Articles  Quantities  Values 

Barley 95137  $76278 

Corn   776984  655805 

Oats 46278  24391 

Rye 249  254 

Wheat 544733  562063 

Totals 

10.  A  manufacturer  sells  automobiles  for  $950  each.  He 
sells  235  machines  in  March,  341  in  April,  462  in  May,  508 
in  June,  and  470  in  July.  If  the  cost  of  manufacturing  and 
marketing  is  $695.45  for  each  machine,  and  the  manufacturer 
replaces  guaranteed  parts  to  the  total  amount  of  $864.79, 
what  is  his  gain  on  the  5  months'  sales  ? 

BUS.    AKITII.  —  3 


34  DIVISION 

Group  4 

1.  A  campaign  committee  sent  out  125,000  pamphlets. 
Printing  cost  §2.10  per  thousand,  postage  1^  each,  and 
addressing  and  mailing  took  33  clerks  5  days  at  $2  per 
day.     Find  the  total  cost  to  the  committee. 

2.  A  man  pays  165  an  acre  for  40  acres  of  land.  He 
buys  at  15^  each  enough  nursery  stock  to  plant  80  trees  to 
the  acre  and  pays  1 220  for  the  labor  of  planting.  For  how 
much  must  he  sell  the  orchard  to  gain  §1200? 

3.  A  steam  shovel  removes  57  cubic  yards  of  dirt  during 
each  hour  of  a  10-hour  day.  Its  operating  cost  is  §13  per 
day  for  wages,  §5.25  for  fuel  and  water,  and  §6.32  for  in- 
cidental charges.  How  much  does  it  cost  to  remove  each 
cubic  yard  of  dirt? 

4.  An  excursion  train  of  12  coaches  travels  144  miles. 
Each  coach  carries  72  passengers  who  pay  §1.50  each  for 
the  trip.  How  much  does  the  railroad  company  receive  for 
each  mile  traveled? 

5.  A  coal  dealer  bought  475  tons  of  coal,  receiving  2240 
pounds  for  a  ton.  If  he  sold  it  at  2000  pounds  per  ton, 
how  much  did  he  receive  at  §7.50  per  ton? 

6.  A  horse  consumes  60  bushels  of  oats  in  a  year,  and 
a  cow  40  bushels.  A  farmer  who  raises  900  bushels  saves 
out  enough  to  feed  4  horses  and  2  cows.  At  50^  per  bushel 
how  much  does  he  receive  for  the  remainder? 

7.  Mr.  Frank  Carter  bought  of  the  Star  Grocery : 

1  qt.  cranberries  at  15^  per  qt. 
1  basket  of  grapes  at  20  j^. . 
2|  lb.  tomatoes  at  15  j^  per  lb. 
8|  lb.  turkey  at  29^  per  lb. 
4  lb.  butter  at  33^  per  lb. 


MISCELLANEOUS  PROBLEMS 


35 


He  tendered  a  twenty-dollar  bill  in  payment.     How  much 
change  did  he  receive? 

8.  Make  out,  extend,  and  foot  a  bill  for  the  following  : 
Chas.  Walters  bought  of  the  Talmadge  Hardware  Company, 
1  handsaw,  12.10;  17  pounds  of  eightpenny  nails  at  7^  per 
pound ;  25  feet  of  rubber  hose  at  18  ^  per  foot ;  35  yards  of 
iron  sheeting  at  25^  per  yard;  60  feet  of  poultry  fence  at 
5^j^  a  running  foot;  2^  gross  of  |  inch  screws  at  92 j^  per 
gross. 

9.  A  dramatic  producer  spent  $4350  for  costumes, 
113,875  for  scenery,  |  945  for  labor,  and  f  6500  for  advertis- 
ing. His  receipts  were  §27,500,  out  of  which  12750  was 
paid  to  the  author  of  the. play  in  royalties.  How  much  did 
he  lose  ? 

10.    Determine  the  balance  in  the  following  trial  balance  of 
a  fire  insurance  company. 

Trial  Balance 

Losses  paid $16785.90 

Losses  not  paid 5210,85 

Premiums  in  hands  of  agents 7892.54 

Capital $200000. 

Surplus 100000. 

Premiums 97500. 

Interest 8942.50 

Commissions -26847.25 

Taxes 1510.83 

Salaries 7428.10 

General  expenses 16582.72 

Investments  and  loans 290150.69 

Office  furniture 2495.10 

Stationery  and  supplies  (inv.) 1828.90 

Accounts  receivable 16825.95 

Accounts  payable 3180.75 

Reserve  for  losses  not  paid 5210.85 

Organization  expenses 1822.03 

Balance 


36  DIVISION 

Group  5 

1.  If  1648  is  the  divisor  and  also  the  quotient  in  a  prob- 
lem in  division,  what  is  the  dividend  ? 

2.  How  many  times  must  27,685,943  be  subtracted  from 
332,231,316  to  leave  0  ? 

3.  From  the  following  schedule  of  property  left  by  a 
testator,  determine  the  share  of  each  of  seven  heirs  who 
share  equally. 

1.  Books  and  library $  2000. 

2.  Personal  effects 750. 

3.  Household  furniture 1000. 

4.  Account  due  Home  Fur.  Co.      ....  $     234.50 

5.  Cash  in  1st  Nat.  Bank 9000. 

6.  Notes  payable 2340. 

7.  750  shares  X  Y  Coal  Co 75000. 

8.  Life  Ins.  Policy .  5000. 

9.  Loan  on  same,  with  int 1200. 

15.46 

10.  Improved  real  estate 85000. 

11.  Mortgage  on  same 12000. 

Balance 


4.  Find  the  total  value  of  the  cotton  exports  to  the  fol- 
lowing countries  :  United  Kingdom,  f  44,580;  Canada, 
1 181,462  ;  Mexico,  f  21,205  ;  Central  American  States, 
$236,259;  Cuba, -"^  113,258;  Haiti,  $56,206;  Brazil,  $10,402; 
China,  $336,243;  Philippine  Islands,  $479,655  ;  other  coun- 
tries, $217,082. 

5.  A  fruit  grower  receives  $  1800  for  his  apple  crop  taken 
from  40  acres  of  orchard,  60  trees  to  the  acre.  His  expenses 
are:  for  pruning,  $90;  for  spraying,  $85;  for  picking  and 
packing,  $  185.  What  is  his  profit  on  the  crop  from  each 
tree  ? 


MISCELLANEOUS  PROBLEMS 


37 


6.  Five  children  have  left  to  them  $3154  each;  one  of 
them  dies,  and  the  remaining  four  divide  the  entire  fortune. 
How  much  does  each  receive? 

7.  From  the  following  find  the  total  amount  of  money  in 
circulation  in  the  United  States  on  Sept.  3,  1912.  Gold 
coin,  1 611,699,253  ;  gold  certificates,  1948,650,439;  standard 
silver  dollars,  171,068,661;  silver  certificates,  f  471,846,931; 
subsidiary  silver,  $146,116,659;  treasury  notes  of  1890, 
$2,875,546;  U.  S.  notes,  $338,613,664;  national  bank  notes, 
$705,622,027. 

8.  In  the  following  table  of  government  disbursements, 
find  the  total  for  each  month,  and  the  total  under  each 
heading : 


1912 
Months 

Civil 

War 

Navy 

Indians 

Total 

Jan. 
Feb. 
Mar. 
Apr. 
May 
June 
July 
Aug. 

$  15702645.70 
13562159.76 
12824104.11 
15906538.27 
13399111.59 
12098976.24 
18698533.93 
17094698.17 

$  11825460.90 
10476877.55 
11371468.21 
12098225.20 
13245913.70 
8463485.21 
15134713.55 
16055472.47 

$  11175174.46 
10750125.72 
10689792.99 
12830351.60 
10068913.22 
10053624.53 
10923328.08 
11370147.05 

$2131068.60 
1353724.31 
2028589.16 
2018908.63 
1423293.35 
2051111.91 
868803.61 
940547.41 

Totals 

9.  What  is  the  government's  average  monthly  expend- 
iture for  civil  purposes  ?  for  the  war  department  ?  for  the 
navy  ?     (Data  in  example  8.) 

10.    How  much  does  the  civil  expenditure  exceed  the  war 
expenditure  for  each  month?     (Data  in  example  8.) 


PROPERTIES   OF   NUMBERS 

39.  The  factors  of  a  quantity  are  two  or  more  quantities, 
which,  when  multiplied  together,  will  produce  the  given 
quantity  ;  e.g.^  8  and  5  are  the  factors  of  15. 

40.  Factoring  is  the  process  of  separating  a  number  or 
quantity  into  its  factors. 

To  THE  Teacher.  Give  the  student  much  drill  on  resolving  num- 
bers into  factors,  and  on  the  Tests  of  Divisibility.  Careful  work  here 
will  save  time  later  in  the  solution  of  problems. 

41.  A  prime  ntmiber  is  one  which  cannot  be  exactly 
divided  by  any  other  number  except  itself  and  1. 

A  prime  factor  is  a  prime  number  used  as  a  factor. 
Numbers  prime  to  one  another  are  such  as  have  no  com- 
mon divisor  other  than  1. 

42.  An  even  number  is  a  number  .exactly  divisible  by  2. 

43.  Tests  of  divisibility  : 

1.  All  even  numbers  are  divisible  by  2. 

2.  If  the  sum  of  the  digits  of  a  number  is  divisible  by  3  or 
9,  the  number  is  divisible  by  3  or  9. 

3.,  If  the  two  right-hand  figures  of  a  number  are  ciphers 
or  are  divisible  by  4,  the  number  is  divisible  by  4. 

4.  If  the  right-hand  figure  of  a  number  is  0  or  5,  the 
number  is  divisible  by  5. 

5.  An  even  number  divisible  by  3  is  also  divisible  by  6. 

6.  If  the  three  right-hand  figures  of  a  number  are  divisible 
by  8,  the  number  is  divisible  by  8. 

7.  When  the  right-hand  figure  of  a  number  is  0,  the  num- 
ber is  divisible  by  10. 

38 


FACTORING  39 

44.  Applying  the  tests  given  above,  find  the  prime  factors 
of  6480. 

5)6480 

6)1296  Q  is  used  as  a  divisor  to  save  time.     The  prime  factors  of 

6)216  6  are  2  and  3.     Therefore,  2x3x2x3x2x3x2x3x5 

6)36  ^^®  ^^^  prime  factors. 
~6 
Find  the  prime  factors  of  : 

1.  32     4.  135     7.  3375     lo.  T4088     13.  3540     16.     8313 

2.  48     5.  144     8.  2028      ii.  15309     14.   1016     17.     3400 

3.  90     6.  676     9.  9261     12.   11190      15.   9664     18.   27783 

45.  If  the  factors  are  alike,  as  3x3=9,  3x3  may  be 
written  3^,  and  read  ''  3  square."  The  2  which  is  written  to 
the  right  and  a  little  above  the  number  is  called  the  expo- 
nent, and  indicates  the  power  of  the  number,  or  the  number 
of  times  it  is  to  be  taken  as  a  factor.  3^  =  3  x  3  x  3,  and  is 
read  "  3  cube."     3*  is  read  "  3  to  the  fourth  power." 

Find  the  value  of  : 

1.  53  4.  34  7.  123 

2.  42  5.  25  8.  142 

3.  73  6.  212  9.  83 

10.  What  does  x^  mean  ?     What  does  b^  mean  ? 

11.  Find  the  factors  oi  x  —  ax. 

x^x  —  ax 


\-a 


Therefore,  the  factors  oi  x  —  ax  are  x  and  1  —  a. 


Note.     No  sign  has  been  used  between  a  and  x  in  ax^  but  multiplica- 
tion is  understood. 

When  no  s'lyn  is  expressed  between  two  letters  or  between  a  number  and  a 
letter,  multiplication  is  understood ;  e.g.,  5  a  means  5  times  a. 


40  PROPERTIES  OF  NUMBERS 

Find  the  factors  of 

12.  P-PRT  14.    ax-hx  16.    5^-5  J5 

13.  B- BR  15.    7 -lb  n.    1  x-\x  ' 

18.    What  does  5  (a  —  b)  mean  ? 

46.  The  sign  V  (called  radical  sign)  indicates  that  one 
of  the  equal  factors  of  a  number  is  to  be  found,  or  in  other 
words,  that  the  square  root  is  to  be  taken;  e.^.,  Vu  means 
the  square  root  of  9,  or  3. 

Note.     For  the  method  of  extracting  the  square  root  see  Appendix. 

47.  A  common  divisor  of  two  numbers  is  a  number  that 
will  exactly  divide  each  of  them. 

48.  The  greatest  common  divisor  (G.  C.  D.)  of  two  or  more 
numbers  is  the  largest  number  which  will  exactly  divide  each 
of  them. 

49.  To  find  the  G.C.D.  of  two  numbers,  divide  the  larger 
by  the  smaller,  tlie  first  divisor  by  the  remainder,  and  so  on 
until  there  is  no  remainder.     The  last  divisor  is  the  G.C.D. 

Find  the  G.  C.  I),  of  576  and  198. 

198)57d(^  Divide  the  larger  number  by  the  smaller. 

^^Q  The  quotient  is  2,  with  a  remainder -of  180. 

180)198(1  Divide  this  remainder  into  the  first  divisor, 

180  198.     The  result  gives  a  remainder  of  18 

18)180(10  which  goes  exactly  into  180.     The  G.C.D. 

IgO  is  *h^  ^ast  divisor,  18. 

If   the  numbers  are  not   too  large,  the   process   may  be 
shortened  as  in  the  following  example. 
Find  the  G.  C.  D.  of  66  and  42. 

42     66 

^  Do  not  indicate  all  the  steps  in  the  division,  but  merely 

the  remainders.     The  last  divisor,  6,  goes  into  18  exactly, 

1§ hence  6  is  the  G.  C.  D. 

6 


SrULTIPLES  41 

The  G.  C.  D.  can  often  be  found  by  inspection.  It  must 
be  a  factor  of  the  difference  between  the  two  numbers; 
e.g.^  find  the  G.  C.  D.  of  24  and  45.  The  difference  between 
them  is  21,  whose  factors  are  3  and  7.  Since  7  is  not  a 
divisor  of  both  numbers,  3  is  the  G.  C.  D. 

Plnd  (by  inspection  whenever  possible)  the  G.  C.  D.  of : 

1.  57,  95  3.    72,  180  5.    48,  72 

2.  85,  119  4.    63,  45  6.    364,  512 

7.  24,  36,  60  9.   24,  132,  144 

8.  144,  111  10.    288,  432 

11.  In  a  sawmill  there  are  three  tree  trunks  of  lengths 
32,  48,  and  80  ft.  What  are  the  longest  uniform  boards 
that  can  be  cut  from  them  without  waste  ? 

12.  A  field  is  160  rods  long  and  80  rods  wide.  Boards 
of  what  length  under  15  ft.  can  be  used  to  fence  it  without 
waste  ?     (1  rod  =  161  ft.) 

50.  A  common  multiple  of  two  or  more  numbers  is  a  num- 
ber that  can  be  divided  by  each  of  them  without  a  remainder ; 
thus,  24  is  a  common  multiple  of  2,  3,  and  4. 

51.  The  least  common  multiple  (L.  C.  M.)  of  two  or  more 
numbers  is  the  smallest  number  that  can  be  divided  by  each 
of  them  without  a  remainder ;  thus,  20  is  the  L.  C.  M.  of  2, 
4,  and  5. 

Find  the  L.  C.  M.  of  14,  49,  77,  and  22. 

_.         .       _  Divide  the  numbers  by  any  prime 

7  )14,  4J,   77,   ^^  fg^^^Qj.  ^^^^  ^. jj  exactly  divide  two  or 

11 )    Z,      7,   11,   11  more  of  them.     Divide  the  resulting 

2)    2,      7,      1,      2  quotient  and  the  undivided  numbers 

X        7       1        1  1"^  ^  similar  way,  continuing  until  quo- 

tients are  found  that  are  prime  to  each 
L.  CM.  =  7  X  11  X  2  X  7,  other.  The  product  of  the  several 
or  1078.  divisors  and  the  last  quotients  is  the 

L.  C.  M. 


42  PROPERTIES  OF  NUMBERS 

Find  the  L.  C.  M.  of  the  following  : 

1.  9,  18,  45  4.    8,  16,  26  7.  4,  6,  30,  72 

2.  46,  92,  128  5.    36,  45,  72,  90  8.  2,  3,  5,  7 

3.  33,  52,  78  6.    5,  8,  12,  20  9.  81,  120,  117 

52.   Cancellation  is  useful  when   the  product  of   several 

numbers  is  to  be  divided  by  the  product  of  other  numbers. 

Divide  the  product  of  15  x  9  by  the  product  of  5  x  3  x  2. 

Divide  any  number  on  one  side  of  the  line 

Jl       «  ^  by  any  number  on  the  other  side  of  the  line. 

AT  ^  *  •    _  z.^  or  4i       When  unable  to  divide  further,  multiply  the 

^  X  p  X  2       2  numerators  together  for  a  new  numerator  and 

the  denominators  for  a  new  denominator. 

Notes.  1.  When  no  uncanceled  number  on  one  side  of  the  line  will 
divide  an  uncanceled  number  on  the  other  side  of  the  line,  divide  by  any 
factor  common  to  both. 

2.  Make  use  of  cancellation  whenever  possible.  Do  not  multiply  or 
divide  numbers  until  you  are  sure  no  cancellation  is  possible. 

Use  cancellation  in  the  following  problems : 

1.  Divide  81  x  25  x  34  x  30  by  21  x  5  x  6  x  17. 

2.  Divide  39  X  91  X  96  by  114  x  95  x  160. 

3.  Divide  64  x  76  x  45  x  68  by  114  x  160  x  30. 

4.  A  large  sheet  of  paper  cuts  into  12  small  sheets.  How 
many  packages  of  480  small  sheets  can  be  cut  from  72,600 
large  sheets? 

5.  A  plot  of  ground  320  rods  by  400  rods  is  laid  off  in 
lots  50  ft.  X  160  ft.     How  many  such  lots  can  be  laid  off  ? 

6.  12  cases  of  books,  140  books  to  the  case,  are  to  be 
repacked  in  cases  holding  only  84  books  each.  How  many 
cases  will  be  required  ? 

7.  If  24  tons  of  coal  cost  $135.75,  how  much  will  60  tons 
cost  at  the  same  rate  ? 


FRACTIONS 

53.  Fractions  are  of  two  kinds,  common  and  decimal. 

54.  The  difference  between  common  and  decimal  fractions 
is  that  a  common  fraction  may  have  any  number  for  its 
denominator,  while  the  denominator  of  a  decimal  fraction  is 
always  10,  or  some  power  of  10,  as  100,  1000,  etc. 

55.  The  denominator  of  a  decimal  is  not  written,  but  is 
indicated  by  the  number  of  places  to  the  right  of  the  decimal 
point;  e.^.,  .1*25  is  read  one  hundred  twenty-five  thousandths 
(iVto)*  1000  is  the  denominator  because  there  are  three 
places  to  the  right  of  the  decimal  point. 

56.  (a)  Common  and  decimal  fractions  are  treated  to- 
gether, because  speed  and  accuracy  in  handling  fractions 
come  from  the  ability  to  interchange  them  rapidly. 

(6)  In  the  work  which  follows,   the  term  "  fraction "  is 
used  to  indicate  common  fractions. 
Illustrations : 


Fractions 

\ 

1 

Decimals 

.5 
A 

.125 
.75 

- 

Read  the 

following  decimals : 

1.    .12 

6.    .036 

11. 

1.001 

2.    .24 

7.    .202 

12. 

10.1 

3.    .225 

8.    .3068 

13. 

548.2375 

4.    .31 

9.    12.35 

14. 

275.125 

5.    .3 

10.    205.001 

43 

15. 

208.08 

44  FRACTIONS 

REDUCTION    OF   FRACTIONS 

57.  I  =  ^\^nd^%  =  l. 

The  forms  of  these  fractions  have  been  changed,  but  not 
their  values,  f  has  been  changed  to  its  equivalent  -^^  ^7 
multiplying  both  numerator  and  denominator  by  4 ;  -^^  ^^^ 
been  reduced  to  its  lowest  terms  |  by  dividing  both  its 
numerator  and  denominator  by  4. 

Note.  Decimal  fractions  cannot  be  reduced  to  their  lowest  terms 
unless  they  are  changed  to  the  form  of  common  fractions. 

58.  The  factor  method. 

Reduce  ^f  |  to  its  lowest  terms. 

To  reduce  a  fraction  to  its' lowest  terms,  di- 
2)132  _  3)  66  _  22      vide  both  terms  by  a  common  factor ;  continue 
2)354      3)177       59      to  divide  by  common  factors  until  both  terms 
are  prime  numbers. 

59.  The  G.  C.  D.  method. 

Reduce  J|f  to  its  lowest  terms. 
155       5  When  the  common  factor  cannot  be  found  by  inspec 


31 


— —  =  —     tion,  find  the  G.  C.  D.  by  §  49  and  divide  both  terms  by 
^^'        *      it. 

60.  To  reduce  a  fraction  to  higher  terms. 

Change  J  to  thirtieths. 

30  _i_  (3  _  5  The  required  denominator,  30,  is  5  times  as  large  as 

5  V  ^       or       the  denominator  6.     Then  if  the  denominator  is  to  be 

^ — -  =  —       made  5  times  as  large,  the  numerator  also  must  be  made 
b  X  5      30      5  ti„jgg  ^g  ^j.gg^ 

61.  To  reduce  a  decimal  to  its  lowest  terms. 
Reduce  .125  to  its  lowest  terms. 

125  _  1  Change  the  decimal  to  the  form  of  a  common  f rac- 


125 


1000      8      tion  and  reduce. 


REDUCTION  OF  FRACTIONS  45 

Reduce  to  their  lowest  terms  (by  inspection  when  possible): 


1-  If 

4. 

II- 

7.     .8 

10.    j\\ 

2-    A 

5. 

U 

8.    .25 

11-   tVVs 

3-    U 

6. 

II 

9.    .285 

12.    .5856 

Reduce : 

13.    -y-  to  36ths 

16. 

^\  to  36ths 

19. 

^\  to  120ths 

14.    1  to  27ths 

17. 

1  to  21sts 

20. 

3-%  to  128ths 

15.    ^  to  52ds 

18. 

1  to  21sts 

21. 

11  to  147ths 

62.  A  proper  fraction  is  a  fraction  in  which  the  denomina- 
tor is  larger  than  the  numerator,  as  |^. 

An  improper  fraction  is  a  fraction  in  which  the  numerator 
is  larger  than  the  denominator,  as  |^. 

A  mixed  number  is  the  sum  of  a  whole  number  and  a  frac- 
tion, as  2J. 

63.  To  reduce  an  improper  fraction  to  a  whole  or  a  mixed 
number. 

Reduce  -Yf^  to  a  mixed  number. 

^2  2 ^_  Divide  the  numerator  by  the  denominator. 

^5  2 

Reduce  to  a  whole  or  a  mixed  number : 

64.  To  reduce  a  mixed  number  to  an  improper  fraction. 
Reduce  4f  to  an  improper  fraction. 

^  Multiply  the  whole  number  by  the  denominator  of  the 

—  fraction  and  add  the  numerator.     Express  the  result  over 

^^  the  denominator. 
J 

14-V-  =  4| 


46  FRACTIONS 

Reduce  to  improper  fractions  (by  inspection  when   pos- 
sible) : 

1.  5f  3.    51                    5.    16J                  7.    24f 

2.  8f  4.    171                6.    75|                 8.    172811 

65.  Interchange  of  fractional  forms. 

(a)  Reduce  ^Ib  to  an  equivalent  decimal. 

.0041  -j-  Annex  ciphers  to  the  numerator  and  divide  by  the 

Q_ioNi  QOOO  denominator.     Put  the  point  of  the  quotient  directly 

QrrQ  above  the  point  of  the  dividend.     Write   the   first 

figure  of  the  quotient  (4)  directly  above  the  last  fig- 

^^^  ure  of   1000  (the  first  part  of  the  dividend  used). 

243  Should  there  be  any  vacant  places  in  the  quotient 

-\-  between  the  point  and  the  first  number,  fill  in  with 
ciphers. 

(6)  Change  .12|  to  its  equivalent  fraction. 

Change  the  decimal  to  a  common 

191 

^Q2       121  x2_   25  _1      fraction  ^^.     Multiply  both  numerator 

100  X  2       200       8      ^j^^  denominator  by  2  (the  denominator 
of  the  fractional  part). 

Interchange  the  following  (by  inspection  when  possible)  : 
1. 

2. 

3-    i 

66.  The  least  common  denominator  (L.  C.  D.)  of  two  or 

more  fractions  is  the  L.  C.  M.  of  the  given  denominators. 

Reduce  J,  f,  |,  .33 J  to  equivalent  fractions  having  the  least 
common  denominator. 

f  ~  1^2  l"!^®  ^'  ^-  ^^-  ^^  ^^^  given  denominators  is  12.     Reduce 

f  =  _9^      each  fraction  to  twelfths. 
12 

•83^  =  A 


i 

4. 

A 

7. 

m 

10. 

.371 

13. 

■•8f 

T»6 

5. 

iV 

8. 

tAo 

11. 

.111 

14. 

.16- 

i 

6. 

a 

9. 

.61 

12. 

.331 

15. 

.33 

ALIQUOT  PARTS 


47 


Reduce  to  least  common  denominators 
1. 

2. 
3. 
4. 


h  1%  i 

5. 

.iH'i.ssi'iV 

1'  2T'  -il 

6. 

12|,  141  18^9^ 

H,  .125,  .61 

7. 

.15,  .625,  .25,  .5 

8i  ^T^c.  3iV 

8. 

13|,  171,  19| 

ALIQUOT   PARTS 

67.  An  aliquot  part  of  a  number  or  quantity  is  a  number 
wliich  will  divide  it  without  a  remainder  ;  e.g.^  2  is  an  ali- 
quot part  of  4. 

68.  The  column  under  numerator  1  in  the  following  table 
gives  the  most  useful  aliquot  parts  of  1 ;  the  rest  of  the  table 
contains  the  decimals  most  frequently  found  in  business  and 
their  fractional  equivalents.  Drill  on  these  until  they  can  be 
given  instantly.  The  top  row  gives  the  numerator  ;  the 
column  at  the  left  gives  the  denominator. 

Table 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

2 

.50 

1.00 

1.50 

2.00 

2.50 

3.00 

3.50 

4.00 

4.50 

5.00 

3 

.33^ 

.661 

1.00 

1.33^ 

1.66f 

2.00 

2.331 

2.66f 

3.00 

3.33^ 

4 

.25 

.75 

1.00 

1.25 

— 

1.75 

— 

2.25 

— 

5 

.20 

.40 

.60 

.80 

1.00 

1.20 

1.40 

1.60 

1.80 

— 

6 

.161 

— 

— 

— 

.831 

1.00 

1.16,1 

— 

— 

— 

8 

.121 



.371 

— 

.62-1 

— 

.871 

1.00 

1.12^ 

— 

9 

.IH 

.221 

.44t 

.551 

— 

.771 

.88| 

1.00 

i.iH 

10 

.10 

.30 

— 

— 

.70 

— 

.90 

1.00 

12 

.08| 

— 

— 

— 

.411 

— 

.58| 

— 

— 

— 

16 

.061 

— 

.181 

— 

.3H 

— 

.43f 

— 

.56i 

— 

69.  The  aliquot  parts  of  10,  100,  or  1000  can  be  found 
from  the  above  table  by  multiplying  the  given  aliquot  parts  by 
10,  100,  or  1000;  e.g.,  the  first  column,  expressed  as  aliquot 
parts  of  10,  would  be  5,  3^,  2.5,  2,  If,  1^,  1^  1,  .831  .621. 


48  FRACTIONS 

EXERCISES 

1.  Construct  tables  similar  to  the  table  in  §  68,  showing 
aliquot  parts  of  10,  100,  and  1000. 

What  fractional  part  of  10  is  each  of  the  following  ? 

2.  2J  7.    .625  12.    1.25 

3.  31  8.    6f  13.    2.50 

4.  11      •  9.     If  14.    5 

5.  .6^  10.    11  15.    6.6f 

6.  1.21  11.    l.66f  16.    2 

What  fractional  part  of  100  is  each  of  the  following  ? 

17.  121-  22.    12.50  27.    16.66| 

18.  33 J  23.    Ill  28.    6.25 

19.  16f  24.    1121  29.    33. 33 J 

20.  66|  25.    116f  3p.    250 

21.  6^  26.    150  31.    1331 

32.  What  decimals  are  equivalent  to  J,  |,  |,  J,  |,   J,  |, 

J_    1? 
11'    9  • 

33.  What  fractions  are  equivalent  to  .5,  .62|,  .12 J,  .44|, 
.66|? 

34.  By  inspection  change  the  decimals  in  the  following  to 
fractional  equivalents  and  give  the  L.  C.  M.  of  the  denomi- 
nators :     .25,  ^,  .33J,  .08f 

35.  By  inspection  change  the  decimals  to  fractional  equiv- 
alents and  give  the  L.  C.  M.  of  the  denominators  :  .37|,  J, 
.18|,  .5. 

36.  What  fractions  are  equivalent  to  .37-|,  .83^,  .62 J,  .31  J,, 
.331  .75,  .5,  .22f? 

37.  What  decimals  are  equivalent  to  |^,  |,  ^,  |,  J,  ^,  |,  |,  f  ? 


ALIQUOT  PARTS  49 


Solve  mentally,  and  find  the  total  amount  in  the  following. 

Use  either  quantity 

or  price  as  an  aliquot  part. 

38. 

39. 

40. 

36  yd.  @  121^ 

81yd.  ©Ill  ^ 

120  acres  @fl25| 

60  yd.  @  331  ^ 

62  yd.  @  61^ 

160  acres  @    150 

48  yd.  @Sy 

126  yd.  @  66f  ^ 

720  acres  @    1121 

160  yd.  ®ey 

144  yd.  @  121^ 

36  acres  @    106^ 

41. 

42. 

43. 

50  yd.  @  48  ^ 

24  bu.  @  11.25 

75   acres  @J|  120 

72  yd.  @12y 

68  bu.  @    1.50 

150   acres  @      64 

250  yd.  @  40  ^ 

72  bu.  @    2.50 

1121  acres®      96 

125  yd.  @  11.60 

160  bu.  @  12.50 

2161  acres®      60 

1250  yd.  @     2.40 

25  bu.  @      .88 

610'  acres®    1121 

70.    Aliquot  parts  applied  to  other  numbers. 

(a)    Separate  68  into  numbers  which  are  aliquot  parts  of  60. 
68  =  60  +  6  +  2 

=  (30  +  (-^0  of  60)  +  a  of  6) 

(5)  Separate  54  into  numbers  which  are  aliquot  parts  of  60. 

54  =  60  -  6 

=  60-(Jo  of  60) 

Separate  the  following  numbers  into  aliquot  parts  of  60 : 

1.  40  4.    75  7.    45  10.    20  13.    100 

2.  12  5.    80  8.    30  11.    66  14.    10 

3.  55  6.    90  9.    72  12.    120  15.    15 

16.    If  the  interest  on  a  note  for  60  days  is  $  72,  find  the 
interest  for  82  days. 

Interest  for  60  days  =172 
Interest  for  20  days  =    24        (20  =  J  of  60) 
Interest  for  _2  days  =      2.40  (  2  =  J^  of  20) 
Interest  for  82  days  =  198.40 

BUS.    ARITH. — 4 


50  FRACTIONS 

If  the  interest  on  a  note  for  60  days  is  190,  find  the  in- 
terest for : 

17.  50  days.  21.      48  days.  25.      80  days. 

18.  96  days.  22.      76  days.  26.      35  days. 

19.  24  days.  23.      42  days.  27.      93  days. 

20.  120  days.  24.    135  days.  28.    180  days. 

29.  Find  the  cost  of  80  pounds  at  45  ^  per  pound. 

80  pounds  @  50  ^  =  $  40      (i  of  80) 

80  pounds  @  _5^  = 4      (5  ^  is  J^  of  50  <^) 

80  pounds  @  45^  =  $36      (By  subtraction) 

30.  Find  the  cost  of  42  yards  at  7 J  ^  per  yard. 

42  yd.  @  10  ^  =  1 4.20     (J^  of  42) 

42  yd.  @2|7=     1.05     (21- ^  =  i  of  10  ^)   . 

42  yd.  @  71  ^  =  $3.15     (By  subtraction) 

Extend  (mentally  whenever  possible)  and  foot  the  follow- 
ing bills: 

31.  32.  33. 

21  lb.  @  16f  ^  200  yd.  @  25  ^    35  bu.  @  60  ^ 
50  lb.  @  92  ^     56  yd.  @  9  ^     8  bu.  @  62^  ^ 

81  lb.  @  %  1.75  44  yd.  @  11  ^  1300  bu.  @  80  ^ 

33  lb.  @  331  ^    16  yd.  @  71  ^  900  bu.  @  66|  ^ 

150  lb.  @  40^     15  yd.  @  13^^  1000  bu.  @  11.031 

50  lb.  @  70^     25  yd.  @  55^  480  bu.  @  $1.12^ 

125  lb.  @  12  ^  116  yd.  @  27 J  ^  480  bu.  @  48|  ^ 
18  1^.  @  22  ^     80  yd.  @  12-|  ^    70  bu.  @  $1.40 

563  lb.  @  50  ^  240  yd.  @  44  ^  1250  bu.  @  70  i 

2000  lb.  @  371^  250  yd.  @  32  ^  1564  bu.  @  75^ 

31J  lb.  @  56  ^  120  yd.  @  75  ^    70  bu.  @  50  ^ 

96  lb.  @  61  ^  250  yd.  @  $  1.25  500  bu.  @  %  2.50 


ADDITION  51 

ADDITION    OF   FRACTIONS 

71.  Fractions  having  the  same  denominator  are  added  by 
writing  the  sum  of  their  numerators  over  the  denominator. 
Thus,  t  +  f  =  f . 

If  the  denominators  are  different,  reduce  the  fractions  to 
tlieir  least  common  denominator.  Always  reduce  results  to 
simplest  form. 

Add  |,  f ,  |,  and  ^\. 
%=    8 


=    9 


By  inspection  the  L.C.D.  is  12.     Write  the  12  as 
shown  in  the  sohition.   Find  the  separate  numerators, 


|-  =  10  writing  them  as  shown.     Add  the  numerators,  writing 

J7    =     7  the  sum  as  the  numerator  of  12.     "  Think  "  all  opera- 

"sT  _  9A      tions,  naming  only  results. 
12  ~  ^6 

72.  To  add  mixed  numbers. 

• 

(a)    Add,       ITx?     6  -^^^  ^^^  whole  numbers.     Add- 

oi       A  ing   the    fractions   by   the    above 

method,  we  find  the  sum   is   ||. 
Express  the  result  in  its  simplest 


'6' 


6f  21 


Change  the  common  fractions 

^iN     All    o<^r»  o4  -in  to  the  decimal  form.     In  chane- 

(b)  Add,  84.16  =    84.16  .     ,      i  ^^  ^i,  •   j    •      ,  ^ 

^  ^  mg|  and  ^totheir  decmial  form, 

io4g  =  lD4.iZ0  carry  out  to  as  many  places  as 

75|^  =     75. 666|  there  are  places  in  the  longest  ex- 

154  =     15.714#         act  decimal.     Add  the  common 

339,665^-^       fractions.      Keep    the     decimal 

points  in  a  perpendicular  line. 

Note.  The  fraction  |f  in  the  above  is  retained  only  in  exact  calcula- 
tions. Ordinarily,  if  this  fraction  is  more  than  |,  1  is  added  to  the  near- 
est figure  and  the  fraction  is  dropped.  The  above  result  would  then  be 
839.666. 

Add  (by  inspection  when  possible)  : 


52 


FRACTIONS 

.15,185.6,106.75         8.    18.195, 

17.206,  73.008 

15f                 10.    448f 

11. 

29356f 

251                        5621 

95465.25 

321                         324,V 

24687.375 

5Sj\                       832.12^ 

68721 

72f                         648J 

58934.53J 

16|                         763 

687293 

12.  How  many  yards  of  silk  are  there  in  the  following 
pieces  36^,  48i,  56^  79?  (The  small  numbers  written,  to  the 
right  and  a  little  above  indicate  quarter  yards.) 

13.  How  many  dozens  are  there  in  the  following  lots,  the 
small  numbers  indicating  twelfths  of  a  dozen:  3^,  5^,  12^,  24^ 

l7^  41, 10  ? 

14.  How  many  pounds  are  there  in  the  following,  the 
small  niimbers  representing  sixteenths  of  a  pound:  198^ 
1975,  20r,  1998,196^? 

SUBTRACTION   OF  FRACTIONS 

73.    In  subtracting  fractions  follow  the  same  rules  as  in 
adding  fractions,  only  subtract  the  numerators, 
(a)  Subtract  |  from  |. 

5     5  Write  the  common  denominator  (8)  as  shown.     Change 

I     Q  each  fraction  to  the  common  denominator,  and  write  the 

^'' —-  numerators  (5  and  2)  as  shown.     Subtract  the  numerators, 

8  writing  the  difference  (3)  as  the  numerator  of  8. 

(5)  Subtract  103.27  from  285^. 

2851     =285.125 

103.27  =  103.27  The  explanation  is  left  to  the  pupil. 

181.855 

Solve  (by  inspection  when  possible)  : 

1-  1-4  2.  f-i  3.  j%-| 


MULTIPLICATION  53 

.     4.    .668 -.005  5.    .25-1  e.    2358.12 -254J 

7.  From  the  sum  of  2895.111  and  3429^  take  the  sum  of 
1537.25  and  2405^5.. 

8.  Add  the  difference  between  400. 37|^  and  281^  to  the 
difference  between  729.831  and  425.5. 

•     9.    From  the  sum  of  3751    728.83^,   .00125,  42387.135 
take  2957^5^. 

10.    From  25  take  the  sum  of  9.45J,  3.128,  and  7.25. 

MULTIPLICATION   OF   FRACTIONS 

74.  To  multiply  fractions,  multiply  the  numerators  for 
the  numerator  of  the  result,  and  the  denominators  for  the 
denominator  of  the  result ;  e.g.^  |  x  |^  =  2^- 

Use  cancellation  whenever  possible. 

(a)  Multiply  I  X  i\  X  If . 
3 
1-  X  —  X  -  =  —  Follow  the  rule  for  cancellation. 

7 

(6)  Multiply  48  x  .66|. 
48       -  —  32  '^^^^  =  t  ^y  ^^®  "  aliquot  parts  "  table. 

(0    Multiply  28  X  |.  5  i3  11.     1  times  28  is  28;  J  of  28  =  7. 

_J_  Then  |  times  28  equals  35  (28  +  7). 

35 

id)  Multiply  28  X  j.  .      ,       ^      ,         .  «o     .     .  . 

^   ^  ^  -^     rj       ^  fisi  less  than  1.     ^  of  28  =  7.     Sub- 

—  tract  7  from  28. 

21 

Note.  Methods  (c)  and  (d)  are  very  rapid  when  the  numerator  is 
1  more  or  1  less  than  the  denominator.  The  same  principle  will  be  used 
in  division. 


54  FRACTIONS 

(e)  Multiply  34.2  by  .357. 

QA  2  Multiply  as  in  whole  numbers.  Point  off  as  many  places 
or  rr  in  the  product  as  there  are  places  in  both  multiplier  and 
multiplicand. 


239  4 
^^  q„^  Note.     To  multiply  by  .01,  .001,  etc.,  point  off  as  many 

places  to  the  left  in  the  multiplicand  as  there  are  places  iti 

12.209  4    the  multiplier. 

Multiply  (by  inspection  when  possible)  : 


1.    j\%  X  12             6. 

58749  X  .0001 

11. 

285.4 

X  .003 

2.    18  X  f                  7. 

.564  X  7.28 

12. 

99  X 

m 

3.     21  X  f                  8. 

.45  X  Hi 

13. 

895  X 

:  9.45 

4.    ,\  X  fl                9. 

96  X  .125 

14. 

fxf 

X  iV 

5-    Ixifxfl      10. 

36  X  -V- 

15. 

3216 

X.625 

75.  To  multiply  a  mixed  number  by  an  : 

integer. 

Multiply  463|  by  12 

. 

463| 

12 

8)36 

41                    Multiplj 

926'             "'"^*^- 

'^  1  by  12;    multiply 

463 

by  12. 

Add  th 

463 

5560| 

76.  To  multiply  a  mixed  number  by  a  fraction. 

Multiply  248|  by  f . 

248f  X  f 
^  Multiply  248  by  f,  by  multiplying  248  by  6  and 

'2±i^  dividing  the  result  by  7. 

5  i^n  =  h'       -A.dd  results. 
i  P     7      7 

213f 


MULTIPLICATION  55 

77.   To  multiply  a  mixed  number  by  a  mixed  number. 

Multiply  41f  by  28f. 
41f 


28f 
328 
82^1, 

29f, 

21 

15 

8 

Multiply  41  by  28. 

41  X  f  =  ^?-S-  or  29f. 

28  X  1=  21. 

Add  results.     (See  §  72.) 

1198       +  If  =  119811 

Solve : 
1. 

342f  X  f 

5.    284fx273f 

2. 

1  X  281f 

6.    466fx3^ 

3. 

t\  X  428| 

7.    225.125x1 

4. 

56|  X  34^ 

8.    328.66fXi9^ 

MULTIPLICATION    OF    COMMERCIAL   FRACTIONS 

78.  The  fractions  most  commonly  used  in   business  are 
halves,  thirds,  quarters,  and  eighths. 

79.  Special  Cases.     To  multiply  mixed  numbers  when  each 
fraction  is  i. 

(a)  When  the  integral  parts  are  the  same  (squaring). 
Multiply  ^  by  41-. 

41  By  partial  products,  |  of  4  =  2,  and  |  of  4  =  2;  combined, 

^^      they  equal  4,  the  original  number.    Multiply  the  number  by  itself 
— ^      increased  by  1  and  add  the  product  of  the  fractions. 

^  5  X  4  =  20,   20  +  i  =  20^. 

(Jb)  When  the  integral  parts  are  different. 
Multiply  41  by  8|. 

4|  Take  \  the  sum  of  the  numbers,    i  of  (4  +  8)  =  6.     (8  x  4) 

_8|       +  6  =  38. 
3gl  The  product  of  the  fractions  =  \.     38  -f  ^  =  38^. 


56  FRACTIONS 

Application  of  aliquot  parts. 

Multiply  650  by  450. 

50  is  i  of  100.  Then  the  problem  is  6^  hundreds 
X  4^  hundreds.  Multiplying  the  mixed  numbers 
gives  29i  ten  thousands  (100  x  100  =  10000).  \ 
of  10000  =  2500.  29  ten  thousands  (290000)  +  2500 
=  292500. 


450  X  450 

35  X  35 

65  acres  at  i85 

55x25 

121  yards  at  81.25 

.95  X  .75 

80.  To  multiply  mixed  numbers  when  the  fractions  are 
alike.  To  the  product  of  the  integers  add  that  fractional 
part  of  the  sum  of  the  integers,  and  annex  the  product  of 
the  fractions. 

(a)  When  the  integral  parts  are  the  same  (squaring). 

Multiply  6^  by  6|. 


^ 

41 

^2 

29i  = 

292500 

Solve 

orally : 

1.    41 

x4l 

2.    31 

x3i 

3.    6| 

x8^ 

4.    51 

x2i 

5.    12^ 

\xV2^ 

6.    91^ 

x7J 

i  of  (6  +  6)  =  3. 

(6) 

<6)  +  3  = 

=  39. 

\x\  = 

iV 

39+tV  = 

=  39^. 

Multiply  6J  by  6f . 
6$ 

"3 

n. 

44A 

1  of  (6  +  6)  =  8. 

(6> 

c6)  +  8: 

=  44. 

fxj 

=  |. 

44  + |: 

=  44|. 

(J)  When  the  integral  parts  are  different. 
Multiply  41  by  6^. 

_6i  iof(4  +  6)=3|.     (4  X  6)  +  3^  =27i.     ^xl  =  ^.    27^^  =  27^ 

27A 


MULTIPLICATION  .      57 

Application  of  aliquot  parts. 

Multiply  625  by  625. 

^'i  6|  hundreds  x  6^  hundreds  =  39y\  ten  thousands. 

6^  ^\  of  10000  =  625.     625  annexed  to  39  ten  thousands 

39  Jg  =  390625      (390000)  gives  390625. 

Notes.  1.  When  the  answer  ends  in  Jg,  annex  0625  to  the  integers 
in  the  product. 

2.  When  the  answer  ends*  in  j%,  as  in  8|  x  8f,  annex  9  times  0625, 
which  is  5625,  to  the  integers  in  the  product. 

Multiply  966|  by  9.66|. 

*^3  Express  the  |  by  as  many  4's  as  there  are  6's  in 

_9J  the  two  factors.     Point  off  as  in  the  multiplication 

93|  =  9344.44|      of  decimals. 

Note.  When  the  decimal  part  is  substituted  for  the  fractional  part, 
add  as  many  numbers  in  the  answer  as  were  displaced  by  the  aliquot  part 
in  both  factors.     (See  966|  x  9.66|.) 

81.   3^,  33J,  333J,  etc.,  can  be  expressed  by  ^;   remember 
that  they  are  the  aliquot  parts  of  10,  100,  1000,  etc. 
Solve  orally : 

825  X  825 

1025  bushels  at  810.25 

931  X  933| 

875  doz.  at  $8.75 

925  X .925 

4.66f  X  4.66f 

825  X  .425 

1275  acres  at  1127.5 

325  rugs  at  f  9. 25 

13.  350  X  350 

14.  286  X  150 

15.  476  X  175 


1. 

8i  X  8-i 

2. 

lOi  X  101 

3. 

91  X  91 

4. 

8|x8f 

5. 

91  X  91 

6. 

4f  x4f 

7. 

81x41 

8. 

12|  X 12f 

9. 

3ix9i 

10. 

36|  X  3f 

11. 

31  X  33J 

12. 

9JX9.3J 

58  FRACTIONS 


DIVISION    OF   FRACTIONS 

82.  The  process  in  the  division  of  fractions  differs  from 
that  in  the  multiplication  of  fractions  in  that  we  multiply 
by  the  reciprocal  of  the  divisor. 

The  reciprocal  of  any  fraction  is  the  fraction  inverted; 
e.g.^  the  reciprocal  of  f  is  |,  the  reciprocal  of  3  (|)  is  ^,  etc. 

83.  To  divide  a  fraction  by  an  integer, 
(a)  Divide  |  by  4. 

(6)  Divide  .0042  by  7. 

OOOfi  Place  the  point  for  the  quotient  directly  above  the 

'  point  in  the  dividend.     Dividing,  7  is  contained  in  0,  0 

7). 004^      times;  7  in  0,  0  times;  7  in  4,  0  times;  7  in  42,  6  times. 

r 

Note.  Observe  carefully  the  position  of  the  decimal  point  in  the 
above  problem. 

Divide  (by  inspection  when  possible) : 

1.  14^17 

2.  lf-^15 

4.  ii^3 

5.  1^5 

6.  .121  ^  4  (aliquots) 

7.  .022-110 

8.  .00044-220 

84.  To  divide  a  mixed  number  by  an  integer. 

When  the  mixed  number  is  small,  change  it  to  an  improper 
fraction  and  divide  as  in  dividing  a  fraction  by  an  integer ; 


9. 

.75-5 

10. 

.0033^3000 

11. 

m^i2 

12. 

.7500-^15 

13. 

Mff-21 

14. 

.881-5-24 

15. 

.56^-18 

16. 

.220122-13 

7)6456| 


DIVISION  59 

(a)  Divide  6456f  by  7. 

Q92  8_  When    the  mixed   number  is  much  larger   than   the 

1^--      divisor,  divide  the  integral  part  of  the  mixed  number  as 
if  there  were  no  fraction. 

7  is  contained  in  6456,  922  times  with  a  remainder 
g  of  2;  then  the  total  remainder  will  be  2|.  Dividing 
21      2f  by  7  gives  ^\. 


(b)  Divide  3.40236  by  52. 

.06543 
52)3.40236 
3  12 

282 

260  Follow  the  same  method  as  in  (b)  §  83. 

223 

208 


156 
156 


Note.  Annex  as  many  ciphers  to  the  dividend  as  are  needed;  they 
have  no  value ;  e.g.,  .5  has  the  same  value  as  .500.  In  annexing  ciphers 
be  careful  not  to  change  the  position  of  the  decimal  point;  e.g.,  2  =  2.00. 

Divide  (by  inspection  when  possible): 

1.   4|-6  9.  448.71f^7 

10.  7.6724^5 

11.  24.66|  ^  8 

12.  2874.5^100 

13.  587.81^\  ^  11 

14.  34.121  ^  8 

15.  5.90^^  -^  11 

16.  48.376-^24 


2. 

8f^l0 

3. 

5|^7 

4. 

686J  -  9 

5. 

8654f  -  7 

6. 

956f  -J-  4 

7. 

48341  -  11 

8. 

478.336  ^  16 

60  FRACTIONS 

85.   To  divide  any  expression  by  a  fraction. 

(a)  Divide  I  by  |.  (6)  Divide  216  by  -i/. 

14=1  ;sJ?xA=9o 

2  . 

(c)  Divide  |  of  |  by  ^  of  |. 
3 
^279_Q5  Invert  all  the  separate  fractions  composing 

4      ^      ^      ^         ^         the  divisor,  and  cancel. 

2 


(^)  Divide  7J  by  if 
2        5 
5252      ^^  _  1 A       Reduce  the  mixed  number  to  an  improper  fraction. 

^  N    T^-    •  1        A14AO  1,       -I  TO         ^^ove  the  decimal  point  in  the 
(e)  Divide   .02408  by  .172    ^.^.^^^  3  p,^^^^  ^  j*;;"  ^;^j,^  ^^ 

'^  make  an  integer  of  it.     Therefore, 

jl72.}i  024.08  the  point  in  the  dividend  must  be 

11  2  moved  3  places  to  the  right.     The 

n  yo  division  is  now  performed  in  the 

same  manner  as  dividing  by  an 

"  ^^  integer.     (See  §83  6.) 

Divide  (by  inspection  when  possible) : 
1.    iV-i\  9.    440.04-1.1 

3.  25.26-1- jS^ 

4.  25.6-^51.2 

5.  .  004 -^  .0002 

6.  ^^i 

7.  31^.5 

8.  625^2.5 


10. 

.24^1.11 

11. 

.0222 -5- .0111 

12. 

.75 -.15 

13. 

48 -A 

14. 

8.5  H- .0017 

15. 

(25ix,V)^(|xi) 

16. 

(lof  f)^(|of  ,7,) 

DIVISION  61 


86.  To  divide  by  a  mixed  number, 
(a)  Divide  364  by  2^. 
52 

Cb)  Divide  6.48^  by  1.3|. 

1.3|       6.48J 
12  12 


16.5       77.80 

The   L.C.M.  of  4  and  3  is  12.     Multiplying 
^''WS  both  dividend  and  divisor  by  12,  gives  the  new 

16^5)77^8.0  dividend  and  divisor,  77.80  and  16.5.     The  divi- 

g(3Q  sion  results  in  a  quotient  of  4.7^\.     (See  §  83  b.) 

1180" 
1155 


16  5         ¥¥ 

(0  Divide  8658.24i\V  ^y  .3|. 
.3f)8658.24J^V 


2361  3.3l||| 
lil)25974i7.2^3^3^ 
22_ 
39 
33 


When  the  fraction  in  the  dividend  is  too  large 
to  handle  by  example  (b)  multiply  both  dividend 
"'  and  divisor  by  the  denominator  of  the  divisor. 

^b  Divide  as  in  (e)  §  85. 

14 
11 
37 
83 


-4  2 
33 


^m=-\\'h     ¥#^ii=iffi 


62 


FRACTIONS 


Divide : 


1. 


196f^6f 


2.  42861^141 

3.  86941^261 

4.  638654if  ^  .39-1 

5.  64.95J^16 


6.  83.65  ^1.7J 

7.  6892752^1-191 

8.  867^191 

9.  9.37|H-.042f 
10.   67.45^111 


87.    Special  methods  of  division  of  fractions. 


(a)    Divide  135  by  .12|. 

135 

8 

1080 


.12|  =  |.     Dividing  by  \  is  the  same 
as. multiplying  by  8. 


(6)    Divide  424  by  25. 

4.24 

4 

16.96 


25  is  \  of  100.  Pointing  off  two  places 
divides  the  number  424  by  100.  Divid- 
ing by  100  makes  the  quotient  \  of  what 
it  should  be,  so  multiply  by  4. 


((?)   Divide  75  by  J. 

75 

25 

100 


I  lacks  just  ^  of  itself  of  being  1. 
Then  add  I  of  the  number  to  itself. 


(d)   Divide  80  by  f 
80 

60 


f  is  just  \  of  itself  larger  than  1. 
Then  subtract  \  of  the  number  from 
itself. 


1.  864 -.16| 

2.  264--.09J-J 

3.  563  ^.16| 

4.  6857^75 

5.  4836^125 


6.  935 ^.88| 

7.  36.54-125 

8.  125 --f 

9.  217 -J 

10.  3568^.901^ 

16.  85.931^^6 


11.  3568 --If 


90^^ 


12.  3568- 

13.  50000-250 

14.  9872 --4 

15.  5893^.36-^^ 


DENOMINATE   NUMBERS 

88.  A  denominate  number  is  a  quantity  used  in  measure- 
ments, the  value  of  whose  unit  has  been  fixed ;  e.g.^  5  feet 
and  3  pounds  are  denominate  numbers  because  the  units, 
feet  and  pounds,  are  fixed  by  law. 

89.  Some  of  the  subjects  to  which  measurements  apply  are 
value,  weight,  length,  area,  capacity,  time,  etc. 

Note.   The  tables  for  the  Metric  System  will  be  found  in  the  Appendix. 

MEASURES    OF   VALUE 

90.  United  States  money. 

Table 

10  mills  (m.)  =  1  cent  (J^) 
10  cents  =  1  dime  (d.) 

10  dimes  =  1  dollar  (,|) 

10  dollars        =  1  eagle 

Note.     The  mill  is  not  a  coin. 

The  following  money  is  now  authorized  by  the  United 
States  Government :  — 

Coins : 
The  copper  one-cent  piece  and  the  nickel  five-cent  piece. 
The  silver  dime,  quarter,  half  dollar,  and  dollar. 
The  gold  quarter   eagle  (12.50),  half  eagle  (f  5),  eagle 
($10),  and  double  eagle  ($20). 

Note.  Uncoined  gold  and  silver  is  called  bullion.  Silver  coins  less 
than  |1  are  legal  tender  to  the  amount  of  1 10;  nickel  and  copper  pieces 
to  the  amount  of  25  cents. 

63 


64  DENOMINATE  NUMBERS 

Paper  Money : 
Silver  certificates  and  gold  certificates. 
United  States  notes  (greenbacks). 
National  bank  notes. 
Treasury  notes  (not  now  issued  but  still  in  circulation). 

91.  Canadian  money  is  the  legal  currency  of  Canada. 

Table 
10  mills  (in.)  =  1  cent  (f ) 
100  cents  =  1  dollar  ($) 

Note.     Canada  also  issues  subsidiary  coins,  the  silver  5^  piece,  10^ 
piece,  20j* piece,  25^  piece,  and  50^  piece. 

92.  The  unit  of  English  money  is  the  pound  sterling  ;  its 
value  in  United  States  money  is  $4.8665. 

Table 
4  farthings  (far.)  =  1  penny  (d.) 
12  pence  =  1  shilling  (s.) 

20  shillings  =  1  pound  or  sovereign  (£) 

93.  The  unit  of  French  money  is  the  franc  ;  its  value  in 
United  States  money  is  i.l93. 

Table 
10  millimes  (m.)  =  1  centime  (c.) 
10  centimes  =  1  decirae  (dc.) 

10  decimes  =  1  franc  (fr.) 

94.  The  unit  of  German  money  is  the  mark  ;  its  value  in 
United  States  money  is  1.238. 

Table 
100  pfennigs  (pf.)  =  1  mark  (M.) 

MEASURES   OF  WEIGHT 

95.  There  are  three  kinds  of  weights  used  in  the  United 
States  :  Commercial,  Troy,  and  Apothecaries'. 

96.  Commercial  or  avoirdupois  weight  is  used  for  all  com- 
mercial weighing,  except  for  weighing  precious  stones. 


TABLES 


65 


Table 


16  drams  (dr.) 

16  ounces 
100  pounds 

20  cwt.  or  2000  lb. 
112  pounds 
2240  pounds 


=  1  ounce  (oz.) 

=  1  pound  (lb.) 

=  1  hundredweight  (cwt.) 

=  1  ton  (T.) 

=  1  long  hundredweight 

=  1  long  ton 

Notes.     1.  The  long  ton  is  used  in  United  States  customhouses,  and  in 
wholesale  transactions  in  coal  and  iron. 

2.     The  commercial  pound  contains  7000  Troy  grains. 

Commercial  Table 
Showing  pounds  per  bushel  of  various  products,  with  exceptions. 


Pounds 

COiMMODITY 

U.  S.  Cus- 

Exceptions 

tomhouse 

States 

Barley 

48 

48 

Ariz., 45;  Ala.,  Ga.,  Ky.,  Pa.,  47; 
Cal.,50. 

Beans 

60 

60 

Ariz.,  55;  N.H.,  Vt.,  Me.,  62. 

Buckwheat    .     .     . 

48 

52 

Cal.,  40;  Conn.,  Me.,  Mass.,  Mich., 
Miss.,  N.Y..  Pa.,  R.I.,  Vt.,  48; 
Idaho,  N.  Dak.,  S.  Dak.,  Okla., 
Ore.,  Tex.,  Wash.,  42;  Ind.,  Kan., 
Minn.,  N.J.,  N.C.,  Ohio,  Tenn., 
Wis.,  50. 

Clover  seed    .     .     . 

60 

60 

N.J.,  64. 

Corn  (in  ear)     .     . 

70 

70 

Miss,,  72;  Ohio,  Ind.,  Ky.,  68. 

Corn  (shelled)   .     . 

56 

56 

Mass.,  50;  Cal.,  52 

Corn  meal      .     .     • 

48 

50 

Ala.,  Ark.,  Ga.,  Fla.,  111.^  Miss., 
N.C.,  S.C,  Tenn.,  48. 

Oats 

32 

32 

Md.,  26 ;  N.  J.,  Va.,  30;  Ida.,  Ore.,  36. 

Onions 

57 

57 

Conn.,  Me.,  Mass.,  Minn.,  N.  Dak., 
S.  Dak.,  Okla.,  Vt.,  52;  Fla., 
Tenn.,  56;  Ind.,  48;  Mich.,  54; 
Ohio,  55;  Pa.,  R.I.,  50. 

Peas 

60 

60 

Potatoes    .... 

60 

60 

Md.,  Pa.,  56. 

Rye 

56 

66 

Colo.,  54;  Me.,  60.      " 

Timothy  seed     .     . 

45 

45 

Ark.,  60;  Okla.,  N.  Dak.,  S.  Dak.,  42. 

Wheat 

60 

60 

BUS.    ARITH. 


66  DENOMINATE  NUMBERS 

Other  Commercial  Measures 

Beef  — barrel 2001b. 

Butter— firkin 56  1b. 

Fish- quintal 1001b. 

Flour  — barrel 196  1b. 

Grain  —  cental 100  lb. 

Nails  — keg 1001b. 

Pork  — barrel 2001b. 

Salt  — barrel 2801b. 

Lime  — cask" 2401b. 

97.  Gross  weight  is  the  total  weight  of  the  goods  and  the 
containing  package,  commonly  called  container. 

98.  Net  weight  is  the  weight  of  the  goods  alone. 

99.  Tare  is  the  allowance  made  for  the  weight  of  the  con- 
taining package. 

100.  Troy  weight  is  used  in  weighing  diamonds,  gold,  sil- 
ver, and  other  precious  minerals. 

Notes.  1.  The  carat  used  in  weighing  diamonds  is  equal  to  3.168 
grains. 

2.  The  term  carat  is  also  used  to  denote  the  Jineness  of  gold,  and 
means  ^\  part.     Gold  18  K.  (carats)  fine  is  ^|  pure. 

Table 

24  grains  (gr.)  =  1  pennyweight  (pwt.) 
20  pennyweight  =  1  ounce  (oz.) 
12  ounces  =  1  pound  (lb.) 


Table  Diamond  Weight 

16  parts  =  1  carat  grain 
4  carat  grains  =  1  carat  (K.) 


101.   Apothecaries'  weight  is  used  by  druggists  and  physi- 
cians in  compounding  and  prescribing  medicines. 

Note.     Drugs,  medicines,   and   chemicals   are  bought  and   sold  at 
wholesale  by  commercial  weight. 


TABLES  67 


Table 


20  grains  (gr.  xx)  =  1  scruple  (sc.  or  3) 
3  scruples  (iij)  =  1  dram  (dr.  or  5) 
8  drams  (viij)  =  1  ounce  (oz.  or  3) 
12  ounces  (xij)  =  1  pound  (lb  or  #) 

Notes.  1.  In  writing  quantities  in  apothecaries'  weight,  the  charac- 
ters denoting  denominations  precede  the  figures,  except  in  pounds. 
The  quantities  are  usually  expressed  in  Roman  characters. 

2.   Fractions  of  a  pound  are  generally  used  instead  of  ounces. 

LONG   MEASURE 

102.  The  statute  mile  of  5280  feet  is  the  legal  mile  in  the 
United  States  and  England. 

103.  The  inch  and  yard  for  common  use  are  divided  into 
halves,  quarters,  eighths,  and  sixteenths.  At  the  United 
States  customhouses  they  are  divided  into  tenths,  hun- 
dredths, etc. 

Table 

12  inches  (in.  or  ")     =1  foot  (ft.  or  ') 
3  feet  =  1  yard  (yd.) 

5^  yards  or  16^  feet    =  1  rod  (rd.) 
40  rods  =  1  furlong  (fur.) 

320  rods  or  5280  feet  =  1  mile  (mi.) 

Notes.  1.  Dimensions  are  written:  first,  length  ;  then,  width  ;  then, 
height  or  thickness. 

2.  The  following  abbreviations  are  used:  a  room  18  ft.  long,  14  ft. 
wide,  and  8  ft.  3  in.  high  may  be  written :  a  room  18'  x  14'  x  8'  3". 

Special  Long  Measure 

1  size  =  I  in.     Used  by  shoemakers. 

1  hand  =  4  in.     Used  in  measuring  the  height  of  a  horse. 

1  fathom  =  6  ft.     Used  in  measuring  depths  at  sea. 

1  knot  (geog.  mi.)  =  1.1522    ly^.^  or  6086  ft.     Used  for  measuring 

distances  at  sea. 
3  knots  =  1  league. 


68  DENOMINATE  NUMBERS 

104.  Sixrveyors*  long  measure  is  used  in  measuring  the 
dimensions  of  land,  etc. 

Notes.  1.  The  unit  of  measure  is  the  Gunter's  Chain,  which  is 
4  rods,  or  66  feet,  long,  divided  into  100  links. 

2.  In  measuring  roads,  etc.,  a  tape  or  chain  100  feet  long  is  used, 
each  foot  divided  into  tenths  and  hundredths. 

Table 

7.92  inches  =  1  link  (1.) 

25  links  =  1  rod  or  pole  (rd.) 

40  rods  or  100  1.  =  1  chain  (ch.) 
80  chains  =  1  mile  (mi.) 


SQUARE   MEASURE 

105.   Square  measure  is  used  in   measuring  the  areas  of 
surfaces,  as  land,  boards,  plastering,  etc. 

Notes.     1.     The  area  of  a  surface  is  found  by  multiplying  the  length 
by  the  breadth. 

2.   Paving,  painting,  etc.,  are  estimated  by  the  square  of  100  square 
feet. 

Table 

144  square  inches  (sq.  in.)  =  1  square  foot  (sq.  ft.) 
9  square  feet  =  1  square  yard  (sq.  yd.) 

30^  square  yards  =  1  square  rod  (sq.  rd.) 

160  square  rods  =  1  acre  (A.) 

640  acres  =  1  square  mile  (sq.  mi.) 


GOVERNMENT   LAND   MEASURE 

106.  The  public  lands  are  surveyed  by  selecting  a  north 
and  south  line  called  a  principal  meridian,  and  an  intersect- 
ing east  and  west  line  called  a  base  line. 

107.  Range  lines  are  lines  running  north  and  south  on  each 

side  of  the  principal  meridian,  at  intervals  of  6  miles.     The 
strips  into  which  the  land  is  thus  divided  are  called  ranges. 


TABLES 


69 


5 

4 

3 

5* 

2 

f 

4 

3 

^I 

1 
Base 

1 

Lin 

^  2 

3 

4 

1 

1 

". 

2 

3 

3 

6 

5 

4 

3 

2 

1 

7 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

19 

20 

21 

22 

23 

24 

30 

29 

28 

27 

26 

25 

31 

32 

33 

34 

35 

36 

A  Township  divided  into  Sections 

108.   Townships  are  formed  by  running  east  and  west  lines 
parallel  to  the  base  line  at  intervals  of  6  miles. 

Notes.     1.    Townships  are  numbered  north  and  south;  ranges,  east 
and  west. 

2.  A  township  is  divided  into  36  sections,  each 
1  mile  square.     Each  section  contains  640  acres. 

3.  A  section  may  be  divided  into  halves  or  quar- 
ters, which  are  named  according  to  their  location 
in  the  section;  thus,  "  E.  (East)  I  of  Sec.  20," 
"  S.  W.  (South  West)  \  of  Sec.  20."  The  halves 
and  quarters  may  be  similarly  subdivided;  thus, 
"  N.  W.  i  of  N.  W.  I  of  Sec.  20."  A  Section 


N.W.  }i 

of 
N.W.  >^ 

Section 
320  A. 

S.  3^of 
N.W.  >^ 

S.W.1^ 
Section 
160  A, 

CUBIC   MEASURE 

109.   Cubic  measure  is  used  in  measuring  the  contents  or 

volumes  of  solids.  Table 

1728  cubic  inches  (cu.  in.)  =  1  cubic  foot  (cu.  ft.) 
27  cubic  feet  =  1  cubic  yard  (cu.  yd.) 

24|  cubic  feet  =  1  perch  (P.) 

128  cubic  feet  =  1  cord  (cd.) 

1  cubic  yard  (of  earth)  =  1  load 

Notes.     1.   A  cord  of  wood  is  a  pile  8'  x  4'  x  4'. 

2.  A  perch  of  stone  is  16^'  x  1^'  x  1'. 

3.  A  cubic  foot  of  water  weighs  62|  pounds. 


70  DENOMINATE  NUMBERS 

MEASURES   OF   CAPACITY 

110.  Liquid  measure  is  used  in  measuring  liquids. 

Table 

4  gills  (gi.)  =  1  pint  (pt.) 
2  pints         =  1  quart  (qt.) 
4  quarts       =  1  gallon  (gal.) 

Notes.     1.   Barrels  are  of  various  sizes,  but  31  ^  gallons  is  a  technical 
barrel. 

2.  The  unit  of  liquid  measure  is  the  gallon  of  231  cubic  inches. 

3.  A  gallon  of  water  weighs  about  8^  pounds. 

111.  Apothecaries*  fluid  measure  is  used  by  druggists  and 
physicians  in  compounding  and  prescribing  liquid  medicines. 

Table 

60  minims  (m.)   =  1  fluid  drachm  (f  5) 

8  fluid  drachms  =  1  fluid  ounce  (f  3  ) 
16  fluid  ounces     =  1  pint  (O.) 

8  pints  =  1  gallon  (Cong.  =  231  cu.  in.) 

Note.     The  fluid  gallon  contains  231  cubic  inches. 

112.  Dry  measure  is  used  in  measuring  grain,  fruits,  etc. 

Table 

2  pints  (pt.)  =  1  quart  (qt.) 
8  quarts  =  1  peck  (pk.) 
4  pecks  =  1  bushel  (bu.) 

Notes.     1.   The  unit  of  measure  is  the  Winchester  bushel,  which 
contains  2150.42  cubic  inches ;  it  is  used  in  measuring  grain,  sand,  etc. 

2.  The   heaped  bushel  contains  2747.71  cubic  inches;  it  is  used  in 
measuring  fruits,  vegetables,  etc. 

3.  Fruits  and  vegetables  are  often  sold  by  the  pound  instead  of  by 
dry  measure. 

4.  The  gallon  dry  measure  contains  268f  cubic  inches. 


TABLES  71 


CIRCULAR   MEASURE 

113.  Circular  measure  is  used  in  measuring  angles  or  arcs 
of  circles. 

Table 

60  seconds    (")  =  1  minute  (') 

60  minutes         =  1  degree  (°) 

360  degrees  =  1  circle  (cir.) 

Notes.  L  The  unit  of  circular  measure  is  the  degree,  which  is 
■^Ijj  of  the  circumference  of  a  circle. 

2.  At  the  equator  1  degree  is  equal  to  69^  statute  miles,  or  60 
geographical  miles  or  knots. 

TIME   MEASURE 

114.  The  length  of  the  solar  year  is  the  exact  time 
required  by  the  earth  to  make  one  complete  revolution 
around  the  sun,  —  365  days,  5  hours,  48  minutes,  46 
seconds  (nearly  365^  days). 

115.  The  solar  year,  divided  into  365  days,  is  called  a 
common  year ;  every  fourth  year  (leap  year)  1  day  is  added 
to  the  month  of  February.  A  little  too  much  is  allowed  in 
this  way,  so  the  centennial  years  not  divisible  by  400  are 
excluded.     (The  year  1900  was  not  a  leap  year.) 

Table 

60  seconds  (sec.)  =  1  minute  (min.) 
60  minutes  =  1  hour  (hr.) 

24  hours  =  1  day  (da.) 

7  days  =  1  week  (wk.) 

100  years  =  1  century  (C). 

Commercial  Table 

30  days   =  1  month  (mo.) 
12  months  =  1  year  (yr.) 


72  DENOMINATE  NUMBERS 

116.  Standard  time  is  the  time  adopted  by  the  railroads 
of  the  United  States  and  Canada,  and  by  nearly  all  the 
people  of  these  countries.  The  country  is  divided  into  four 
time  belts,  each  extending  1^-  degrees  east  and  west  from  the 
meridians  75,  90,  105,  and  120,  west  of  Greenwich.  Since 
there  is  just  a  15-degree,  or  1-hour,  difference  between  each 
meridian,  a  difference  of  1  hour  in  time  is  made  between 
each  time  belt.  The  time  of  the  75th  meridian  is  called 
Eastern  Time ;  the  90th  meridian.  Central  Time ;  the  105th 
meridian,  Mountain  Time  ;  the  120th  meridian.  Western  or 
Pacific  Time. 


MISCELLANEOUS   MEASURES 

117.  Counting. 

Table 


12  units     =  1  dozen  (doz.) 

20  units     =  1  score 

12  dozens  =  1  gross  (gro.) 

12  gross     =  1  great  gross  (gt.  gro.) 


118.  Paper. 


Table 

24  sheets     =  1  quire  (qr.) 
20  quires     =  1  ream  (rm.) 

2  reams     =  1  hiindle  (bdl.) 

5  bundles  =  1  bale  (bl.) 

Note.     Paper  is  often  sold  in  "  reams  of  500  sheets." 

119.  Printers*  measure  makes  use  of  two  units,  viz. :  point 
and  pica. 

Table 

A  point     =  ^^  of  an  inch 
A  pica        =  ^  of  an  inch 
The  agate  =  5^  points 


ADDITION  AND  SUBTRACTION  73 

REDUCTION   OF   DENOMINATE   NUMBERS 
120.   Descending  reduction. 

Reduce  £  5  Is.  Sd.  2  far.  to  farthings. 

£  s.         d.        far. 

5        7      8      2 
20 
1075.  (5x20) +  7  =  107.. 

12 


1292(^. 

4 

5170  far. 


(107  X  12)  +  8  =  1292^/. 
(1292x4)  +2  =  5170  far. 


121.  Ascending  reduction. 

Reduce  59  pt.  dry  measure,  to  higher  denominations. 

2)59 

8)29  qt.  +  1  pt.      ,  ^^^^f;  f  ^/  \  ^\^''  =  \  ^^;)  '  "^'^^  ''  ^y 
^ —  ^  ^  8 ;  result,  3  pk.,  5  qt.,  and  1  pt. 

8  pk.  +  5  qt. 

ADDITION  AND   SUBTRACTION   OF  DENOMINATE 
NUMBERS 

122.  (a.)    Add: 

Add  (upward)  the  farthings  as  fol- 
^  «•  ^-         far.  lows :    3  +  1  =  4,   check  because    4   far. 

3  6  5  2  make  Id. ;    continuing,  1+2  =  3,  write 

4  GsJ        1  down  3. 

3  4  j^  Add    Id.    (carried)    +2  +  4  +  6  =  13 

n  1  o  q  =  Is.  Id.,  check ;  continuing,  1+5  =  6, 

; write  down  6.     Perform  the  rest  of  the 

y  io  O  o  addition  in  a  similar  way.     Result,  £  9 

15s.  M.  3  far. 
(6.)    Subtract: 

Since  3  far.  cannot  be  subtracted  from  1  far., 

^^      y      ,.      ^       borrow  Id.,  which  makes,  in  all,  5  far.;  5  f ar. — 

lb      »      d      1       g  ^^^.  ^  2  far.     Having  borrowed  Id.,  2d.  is  left  in 

O     0      ^     ^       the  minuend ;  2-2  =  0.     Perform  the  rest  of  the 

11      8      0      2       subtraction.     Result  :£  11  8s.  2  far. 


£ 

s.        d. 

far. 

2 

7     8 

2 
12 

74  DENOMINATE  NUMBERS 

MULTIPLICATION   AND   DIVISION   OF   DENOMINATE 
NUMBERS 

123.    (a).    Multiply  £2  78.  M.  2  far.  by  12. 

2  far.  X  12  =  24  far.,  or  Qd.  (12  x  8rf.)4-  6r/.= 
102^/.,  or   85.   6^/. ;    write    6    under   the   pence. 
Perforin    the    rest    of    the    multiplication    in   a 
2y      ][2      6        0       similar  way.     Result:   £28  V2s.  Qd. 

(6).    Divide  £12  lis.  2d.  by  9. 

Divide  £12  by  9  =  1,  with  a  remainder 

£        8.        d.       far.      of  £3.     Reduce  the  £3  to  shillings;   thus, 

*  9)12      11        2  (3  X  20)  +  11  =  71.     7\s.  -^9  =  7,   rem.   85. 

1        7     10     34       (8  X  12)+  2  =  98,  etc.     Result:  £1  7s.  lOd. 

3|  far. 

EXERCISES 

1.  Change  <£  4  58.  to  United  States  money. 

2.  How  many  farthings  are  there  in  200  marks  ? 

3.  Divide  £  18  178.  lid.  by  15. 

4.  What  is  the  cost  of  7  bu.  of  cherries  at  12^  a  quart? 

5.  Find  the  cost  of  2  lb.  10  pwt.  of  ore  at  8^  per  grain. 

6.  Multiply  24  bu.  3  pk.  5  qt.  by  16. 

7.  Reduce  3  T.  5  cwt.  15  lb.  10  oz.  to  drams. 

8.  What  is  the  value  of  a  diamond  weighing  ^g  of  a  carat 
at  il25  per  carat? 

9.  Reduce  38  lb.  to  grains,  apothecaries'  weight. 

10.  A  farm  is  24  ch.  15  1.  long,  and  32  ch.  14  1.  wide. 
How  many  rods  of  fence  will  be  required  to  inclose  it  ? 

11.  Add :  1  mi.  85  rd.  5  yd.,  3  mi.  17  rd.  4  yd.  2  ft.  9  in., 
4  mi.  17  rd.  1  ft.  10  in. 

12.  Read:  S.  1  of  S.E.  1  Sec.  33. 


MULTIPLICATION  AND  DIVISION 


75 


13.  How  many  acres  are  there  in  a  field  200  rd.  long  and 
27  rd.  wide  ? 

14.  How  many  barrels  of  water  can  be  contained  in  a 
tank  8'  3"  x  3'  9"  x  8|'  ? 

15.  From  a  farm  containing  45  A.  72  sq.  rd.,  a  lot 
35'  X  165'  was  sold.     How  much  land  was  left? 

16.  A  man  wishing  to  travel  abroad  changed  flOO  to 
English  money,  |100  to  French  money,  and  flOO  to  German 
money.     How  much  money  of  each  kind  did  he  receive  ? 

17.  A  man  bought  a  farm  located  as  follows :  N.  |  of 
N.E.  ^,  Sec.  4,  T.  15,  North  R.  5  E.  How  many  rods  of 
fence  are  required  to  inclose  it? 

18.  Find  the  value  in  United  States  money  of  the  follow- 
ing: 


Books 


Lodge  of  Edinburgh      .     .     . 
Defoe's  Robinson  Crusoe  .     . 

Robert  Burns 

Philosophical  Works  of  Bacon 
Henley  on  Burns      .... 

Early  Printing 

Freemasonry  ...... 

Postage 

Total 


d. 


10 

6 

4 

6 

6 

6 

10 

6 

2 

0 

3 

6 

6 

6 

10 

0 

19.    Extend  and  foot  the  following  bill 


^  oz.  iodoform                                                    @ 
1  lb.  abs.  cotton 

70 
30 

1  pt.  cresol  comp. 

^  lb.  bismuth  subnitrate 

\  lb.  bismuth  subgallate 

50 
60 
60 

Total 

76  DENOMINATE   NUMBERS 

20.  A  man  bought  a  portrait  in  Paris,  paying  12114  francs 
8  centimes  for  it.  What  was  its  value  in  United  States 
money  ? 

21.  How  many  barrels  of  flour  can  be  made  from  2000 
bu.  of  wheat,  if  1  bu.  will  make  42  lb.  of  flour  ? 

22.  What  is  the  value  of  an  18-carat  gold  case,  weighing 
50  pwt.,  at  80^  per  pennyweight  of  pure  gold  ? 

23.  Together  four  men  own  228f  bu.  of  potatoes.  If  A 
owns  75  bu.  3  pk.,  B  owns  52  bu.  3J  pk.,  and  C  owns 
17^  bu.,  how  much  does  D  own  ? 

24.  Reduce  £  27  17«.  Sd.  2  far.  to  farthings. 

25.  How  much  are  £  25  wortli  in  United  States  money  ? 

26.  How  many  dollars  are  there  in  30  marks  ? 

27.  How  many  pounds  sterling  are  there  in  500  marks  ? 

28.  A  man  bought  5  pairs  of  gloves  at  5  francs  per  pair, 
and  a  hat  for  15  francs.  He  tendered  in  payment  £  2.  How 
many  francs  did  he  receive  in  change  ? 

29.  How  many  pounds  will  1000  silver  dollars  weigh,  1 
dollar  weighing  412J  gr.  ? 

30.  A  coal  dealer  bought  1000  T.  of  coal  at  f  6  per  long 
ton,  and  retailed  it  at  $8  per  short  ton.     What  was  his  gain  ? 

31.  A  merchant  bought  goods  amounting  to  X6000  8«. 
After  selling  part  of  the  goods  for  X5000  6«.  6d.,  he  found 
he  had  remaining  one  third  of  the  original  purchase.  Did 
he  gain  or  lose  on  the  part  sold,  and  how  much  ? 

32.  A  pupil  gets  the  following  grades  in  his  school  work 
for  the  first  term  :  English,  83  ;  arithmetic,  89 ;  history,  92 ; 
science,  84.    Find  the  average  grade  of  his  work  for  the  term. 

33.  Find  the  average  yearly  production  of  oats  in  the 
United  States  from  1900  to  1910,  the  figures  given  being 
millions  of  bushels :  809,.  736,  987,  784,  894,  953,  964,  754, 
807,  1007,  1126. 


BY  ALIQUOT   PARTS  77 

34.  A  grocer  bought  50  qt.  of  cranberries  at  9^  per 
quart,  dry  measure.  He  sold  them  at  11^  per  quart,  liquid 
measure.  How  much  more  did  he  gain  than  he  would  have 
gained  had  he  sold  them  by  dry  measure  ? 

35.  An  automobile  consumes,  on  the  average,  1|-  gal.  of 
gasoline  per  day.  If  gasoline  costs  18^  per  gallon,  find  the 
cost  of  the  gasoline  consumed  from  Feb.  5th  to  Nov.  26th, 
if  the  machine  is  run  6  days  out  of  every  7. 

36.  A  farmer  sold  3  loads  of  potatoes  containing  respec- 
tively 54  bu.  17  lb.,  42  bu.  41  lb.,  and  60  bu.  28  lb.  What 
did  he  receive  at  80^^  per  bushel  ? 

37.  A  farmer  sold  5  loads  of  wheat,  the  weights  in  pounds 
of  the  various  loads  being  as  follows  : 


Weight  of  Wagon  Loaded 

Weight  of  Wagon 

7625 

3870 

7308 

3728 

7000 

3709 

6968 

4000 

7628 

3910 

How  many  pounds 

did  he  sell  ? 

DENOMINATE   NUMBERS   BY  ALIQUOT  PARTS 

124.    Grain  is  generally  priced  by  the  bushel,  but  sold  by 
the  pound. 

1.    Find  the  value  of  24000  lb.  of  wheat  at  95^  per  bushel. 

There  are  60  lb.  in  a  bushel 

of  wheat;  then  60^  per  bushel 

would  be  1^  per  pound.     Point 

$240,  value  at  60^  per  bushel      ^^  two  places  in  the  number  of 

120,  value  at  30^  per  bushel      pounds  to  find  the  value  at  60^ 

20,  value  at  _5^per  bushel     per  bushel  =  1240.    |  of  $240 

1380,  value  at  95^  per  bushel     ^^^^^^  ^^^^  ^^^  ^^^^^  ^^  ^  ^^  ^0^' 

or  W  per  bushel;  ^  of  |120 
would  give  the  value  at  |  of  30^, 
or  o^  per  bushel. 


78 


DENOMINATE  NUMBERS 


2.  What  is  the  value  of  24000  lbs.  of  coal  (retail)  at  18 
per  ton  ? 

24.000  Point  off  3  places  to  show  the  number  of  thousands  of 

4  pounds.     Multiply  by  ^  the  price,  for  f  8  per  ton  is  ^4 

|i96.  P®^  ^^^^  pounds. 

3.  Extend  and  foot  the  following  bill  of  feed : 


No.  OF  Lbs. 

Article 

Prick 

Value 

84654 

Hay 

^  14  per  ton 

12570 

Bran 

$  18  per  ton 

546570 

Corn  (in  ear) 

40j«  per  bushel 

685470 

Straw 

^  6  per  ton 

40020 

Chop 

§  25  per  ton 

68400 

Oats 

30^  per  bushel 

Total 


4.    Find  the  value  of  the  following  shipment : 


Produce 


Wheat  .  . 
Wheat  .  . 
Clover  seed  . 
Potatoes  .  . 
Onions  .  . 
Beans  .  .  . 
Corn  (shelled) 
Barley  .  . 
Timothy  seed 
Rye      ... 


Total 


Weight  in  Lbs. 


76350 
74000 
36540 
75640 
32400 
48600 
78400 
38000 
48200 
60000 


Pbice  per  Be. 


76j? 
70j« 
$3.00 
90j« 
W^ 
85^ 

30j^ 
J52.00 
56j? 


Value 


GRAPHS 


125.  A  graph  is  a  diagram  showing  fluctuations,  such  as 
variations  in  temperature,  rise  and  fall  of  prices,  etc. 

The  temperature  chart  shows  variations  in  temperature 
from  6  A.M.   to  6  p.m.     The  hour  is  indicated  by  the  row 


A.M. 


10 


12 


3 


70 


50 


40 


^v 


:?: 


Temperature  Chart 

of  figures  along  the  top  ;  the  temperature  is  indicated  by 
the  vertical  column  at  the  left. 
Illustrate  graphically  : 

1.  The  varying  price  of  wheat  for  the  years  1900  to  1911, 
the  prices  for  the  respective  years  being  as  follows  :  1900, 
611^;  1901,  631^;  1902,671^;  1903,  70|y  ;  1904,  811^; 
1905,  77|^;  1906,  69y ;  1907,  71^;  1908,  84|-^;  1909, 
99y  ;   1910,  891^  ;   1911,  83-iy. 

2.  The  production  of  corn  in  the  United  States  for  the 
years  1900  to  1910,  the  figures  given  indicating  millions  of 
bushels  :  1900,  2105  ;  1901, 1522  ;  1902,  2523  ;  1903,  2244  ; 

79 


80 


GRAPHS 


1904,  2407  ;  1905,  2707  ;  1906,  2927  ;  1907,  2592  ;  1908, 
2668  ;  1909,  2772  ;*  1910,  3125. 

To  THE  Pupil.  On  a  sheet  of  graph  paper  keep  a  daily  record,  after 
your  work  has  been  checked  in  class,  of  problems  solved  correctly. 

Problems  missed  should  be  worked  after  they  have  been  explained  in 
class.  Then,  by  means  of  a  dotted  line,  indicate  the  percentage  of  prob- 
lems so  corrected.     This  line  should  not  show  much  variation. 

3.  The  following  graph  illustrates  a  record  kept  for  three 
weeks  : 


loo 


90 


70 


50 


40 


20 


10 


M  i  1 T 1 ' ' 1 Ti  1 1 1 

1     111 

1     /  1  (i 

t           it  j  i: 

I    [       it  2  an 

I-JL       ■  T  7i  v\ 

i  /! '       1  M     'A  '/  1 

\1vA     1tI    !  A   1 

-    t  a  t  il 

1  U  t    '  t 

...    I  rJL  It 

I    X  ti  It 

-EI  tit  tl 

I    t jt      ■f'" 

t    t  t      M 

t  T      r   t        "ii" 

h  1    H  :;      1u 

h        \^            ^ 

h  r~i       ^ 

Tl 

^l^ 

T  1 

"     11 

ti 

xi 

t  1            n 

l~i      tT 

|--j       T"!^ 

^4      1  + 

1-^     li 

r1     it 

r  1       iT 

tj      jI 

tl     3t 

tl      jt 

It      It 

It      11 

\T     ^r 

M       ^ 

At        I 

%    -t    i- 

-  _  __ 

Week 

Day 

WORKKD 

MlSSKD 

Made  Up 

%  Madk  Up 

Men. 

10 

0 

Tues. 

8 

2 

1 

Wed. 

9 

1 

1 

50 

Thurs. 

6 

4 

2 

100 

Fri. 

10 

0 

2 

60 

Mon. 

7 

0 

0 

0 

Tues. 

6 

0 

1 

50 

2 

Wed. 

8 

2 

1 

100 

Thurs. 

9 

1 

2 

100 

Fri. 

7 

3 

0 

0 

Mon. 

7 

3 

3 

75 

Tues. 

9 

1 

4 

100 

3 

Wed. 

8 

2 

1 

100 

Thurs. 

8 

0 

1 

50 

Fri. 

7 

0 

1 

100 

Explanation.  On  Monday,  first  week,  no 
problems  were  missed,  so  the  solid  line  starts 
at  100%.  On  Tuesday,  80%  of  the  assign- 
ment was  correct.  On  Wednesday,  one  prob- 
lem of  those  missed  on  Tuesday  was  made  up 
(50  %).  On  Thursday,  the  remaining  problem 
missed  on  Tuesday  and  the  one  missed  on 
Wednesday  were  worked  (100%),  etc. 


GRAPHS 


81 


4.    The  following  illustration  shows  in  a  graphical  way  the 
percentages  of  investment  on  an  80-acre  farm : 


Land  and  Outbuildings 

Dwelling 

Stock  .     .     

Machinery  and  Iraplenaents 


83i  %  of  the  total  investment 

2|% 


5.    The  following  is  a  graphical  representation  of  the  profits 
of  Oregon  farmers  on  farms  of  different  size. 


'\TH      \      2^     \      3^      \     A^    ^i^    ^^     1     ^^ 

8^ 

9^ 

10^ 

III          lE^^I 

■ 

^^^^^ 

1          ^^^^^^^" 

5  to  20   A, 

21  to  80   A, 

81  to  160  A, 

161  to  320  A 

OVER  320 A, 


6.  A  farmer  who  keeps  a  careful  estimate  of  the  cost  and 
returns  on  all  his  crops  finds  that  wheat  makes  him  7% 
profit,  corn  6 J  %,  oats  5  %,  and  apples  10  %.  Illustrate 
his  profits,  graphically,  as  in  example  5. 

BUS.    ARITH. — 6 


82  GRAPHS 

7.  Draw  a  graph  similar  to  the  one  found  in  example  4, 
which  will  show  approximately  the  following  family  expendi- 
tures. „    ,      , 

Heat  and 

Rent     Household    Clothes    Light    Miscellaneous 
%  of  income  20  25  15  5  30 

spent 

Is  the  balance  which  is  saved,  represented  on  the  graph  ? 

8.  On  a  farm  of  3*20  acres  the  following  percentages  of  in- 
vestment are  made: 

Land  and  Outbuildings 75  %  of  total  investment 

Dwelling 3% 

Stock 19% 

Machinery  and  Implements  ....      3% 

Represent,  approximately,  the  above  percentages. 

9.  The  following  is  a  graphical  representation  of  the  "  Mean 
Monthly  Temperatures  "  for  certain  towns  in  Oregon  as  shown 
by  the  Oregon  Agricultural  College. 


??< So z 


a<o3DujCO 


sllil=is8l 


NEWPORT 


CORVALLIS 


JACKSONVILLE 


PENDLETON 


1.  What  towns  have  the  same  March  temperature  ? 

2.  Which  town  has  the  coldest  January  temperature  ? 

3.  What  is  the  coldest  temperature  recorded  ? 


MISCELLANEOUS  PROBLEMS 


83 


10.    Represent  in  a  way  similar  to  that  used  in  example  9  the 
"Mean  Monthly  Rainfall"  as  shown  in  the  following  statistics: 


Jan. 

Feb. 

Mar. 

Apr. 

May 

June 

July 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Town 
A 

10  in. 

8^  in. 

Tin. 

6  in. 

4  in. 

2  in. 

hin. 

iin. 

2iin. 

^m. 

Sin. 

7  in. 

Town 
B 

6  in. 

61  in. 

4  in. 

21  in. 

2  in. 

lin. 

iin. 

iin. 

1|  in. 

Sin. 

6  in. 

6  in. 

Town 
C 

lin. 

lin. 

lin. 

h  ^^• 

lin. 

iin. 

iin. 

iin. 

lin. 

lin. 

iin 

^in. 

MISCELLANEOUS   PROBLEMS 
Gkoup  1 

1.  Find  the  prime  factors  of  7892,  of  5280,  and  of  754. 

2.  Find  the  factors  of  c  +  cr,  of  6  a;  -f  6  ?/,  and  of  pr  -\-p. 

3.  Find  the  G.  C.  D.  of  326,  140,  and  168. 

4.  A  farmer  has  4  farms  containing  respectively  160  A., 
240  A.,  280  A.,  and  300  A.  If  he  divides  the  farms  into 
equal  parcels  containing  the  largest  number  of  acres  possible, 
how  many  acres  will  there  be  in  each  parcel  ? 

5.  Find  the  L.  C.  M.  of  16,  64,  80,  144. 

Use  cancellation  in  the  following  • 

6.  Divide  78  X  96  X  54  X  160  by  26  x  16  x  56  x  72. 

7.  Divide  121  X  66|  x  100  by  111  x  621  x  16|. 

8.  A  man  bought  a  piece  of  ground  380  rd.  long  and  140 
rd.  wide,  paying  $  125  an  acre.     How  much  did  it  cost  him  ? 

9.  A  man  buys  a  plot  of  ground  100  rd.  long,  lying 
between  two  streets  335  ft.  apart.  How  much  does  it  cost 
him  at  f  500  an  acre  ? 

10.    How  many  cords  of  wood  are  there  in  a  pile  70  ft. 
long,  10  ft.  high,  and  6  ft.  wide  ? 


84 


GRAPHS 


Group  2 

1.  Solve    mentally,    6^  X  Q^  ;     550x550;      .85  x  .65  ; 
f  X  8|. 

2.  Add  94|,  1521,  736 J,  55|,  92 J,  and  14.5. 

3.  Multiply  3624  by  563f . 

4.  Divide  87.478  by  3.81. 

5.  Divide  94358.13J  by  .18|. 

6.  Divide  15  by  .121 ;    by  .16| ;  by  .111 ;   and  by  .621 

7.  Extend  and  foot  the  following  bill  : 


203  yd.  muslin  @  lljf^    .     , 
197  yd.  cotton  goods  @  5J^ 
201  yd.  madras  @11^      . 
108  yd.  denim  @  IS^^      .     . 
216  yd.  silk  @  92j^       .     .     . 


8.    Extend  and  foot  the  following  bill 


72 J  lb.  cheese  @  17}f  . 
113^16.  butter  @  25i  J*  .  , 
203 J  lb.  live  geese  @  12^^ 

63    lb.  ducks  @  13^  ^  .     , 


9.    1  bought  348  eggs  for  $4.35,  and  sold  them  at  24^  per 
dozen.     How  much  did  I  gain  ? 

10.    How  much  will  4 J  bu.  of  apples  cost  at  25^  per  talf 
peck?  1: 

Group  3 

1.  What  aliquot  part  of  112^  is  121  ?    What  part  of  |  is  J? 

2.  What  fractional  part  of  a  number  is  the  number  plus 
f  of  itself.     What  fractional  part  of  200  is  275? 

3.  What  is  the  cost  of  five  60-lb.  tubs  of  butter  at  33 J  ^ 
per  pound? 


MISCELLANEOUS  PROBLEMS 
4.    Extend  and  foot  the  following  bill : 


85 


7^  lb.  galv.  3d  nails  @  fi|  J^ 

3|  lb.  sash  cord  @  35  ^ 

24  8-lb.  weights  @  -^1.40  per  hundredweight 

16  sash  locks  @  75^  dozen 

1 1  doz.  W.  S.  bolts  @  20  J^  dozen    .     .     .     . 

17  pr.  3|  X  3|  butts  @  12i  ^ 

10  door  locks  @  33^  f' 

•5  oz.  S.  C.  irons  @  6J^  ounce 

25  lb.  putty  @  41  f       

12  24"  X  30"  glass  @  h1\f 

7  12"  X  28"  glass  @  ]6|^ 

3.1  lb.  brads  @  8i  J^ 


5.  After  making  the  proper  form,  extend  and  foot  the 
following  bill : 

On  July  10,  1913,  Howe  Bros,  sold  to  M.  S.  Scott,  3|  dozen 
^-qt.  pans  6f"  X  2J'^  at  22^  per  dozen;  15  l|-qt.  pans  Tf' 
X  3",  at  331 1^  per  dozen  ;  5  wash  boilers  22|'^  xl2^^  at  113.50 
per  dozen;  9  8-qt.  galv.  pails,  at  $1.35  per  dozen;  6  12-qt. 
pails  at  il.75  per  dozen. 

6.  After  making  the  proper  form,  extend  and  foot  the 
following  bill : 

On  Oct.  21,  1913,  the  Richardson  Rug  Co.  of  Chicago, 
sold  to  McAllister  and  Co.,  Vincennes,  Ind.,  24  Axminster 
rug«  27"  X  54'',  at  f  1.50  each  ;  18  Axminster  rugs  30''  x  60", 
at  i53.25  each;  9  Wilton  velvet  rugs  36"  x  72",  at  $2.75 
each  ;  16  Tapestry  Brussels  rugs  27"  x  54",  at  $.75  each  ;  24 
Body  Brussels  rugs  6'  x  9',  at  $12.50  each  ;  6  Body  Brussels 
rugs  9'  X  12',  at  $20  each;  44'  of  hall  runner  27"  wide,  at 
331^  per  ft. 

7.  The  interest  on  $250  for  60  da.  is  $2.50.  Find  the 
interest  for  45  da.  ;   for  75  da.  ;   for  130  da.  ;    for  190  da. 


86  GRAPHS 

Make  the  extensions  mentally,  and  find  the  total  amount 
in  each : 

8.  9. 

12  yd.  at  12|^  1  gal.  at  $1.90 

96  yd.  at  6y  i  gal.  at  98^ 

45  yd.  at  10^  2J  gal.  at  f  1.90 

25  yd.  at  19^  3.}  gal.  at  12.50 

26  yd.  at  15^  12^  gal.  at  15.50 

10.    Extend  and  foot  the  following  bill ; 


2^  doz.  9"  plates  @  f$  1.85  per  J  dozen 
6f  doz.  10"  plates  @  .^2.20  per  dozen 

10  lOi"  plates  @  !$2.95  per  J  dozen     . 

11  doz.  8^"  plates  @  -^1.35  dozen  .     . 
i  doz.  7i"  plates  @  $1.36  dozen    .     . 


Group  4 

1.  A  man  works  overtime  1  hr.  and  15  min.  each  day 
for  3  da.,  and  1  hr.  and  40  min.  each  day  for  5  da. 
At  36^  per  hour  for  overtime,  how  much  extra  has  he 
earned  in  the  8  da.? 

2.  A  race  horse  trots  a  mile  in  2  :  04.  How  many  yards 
does  it  travel  in  10|  sec.  ? 

3.  A  railroad  gains  in  elevation  1232  ft.  in  a  distance 
of  6  mi.,  3520  ft.     What  elevation  is  gained  per  mile  ? 

4.  An  automobile  circles  a  half-mile  track  in  44  sec. 
How  many  feet  does  it  travel  per  second  ?  What  is  its  speed 
per  hour  ? 

5.  A  train  travels  a  mile  in  52  sec.  What  is  its 
speed  per  hour? 

6.  A  dealer  bought  22  gal.  of  milk  at  13^  per  gallon, 
and  sold  it  5^  per  glass  of  |  pt.     What  is  his  gain  ? 

7.  I  owe  £13  8*.  Id.  in  England,  1000  francs  in  France, 


MISCELLANEOUS  PROBLEMS  87 

and  324  marks  in  Germany.     What  is  my  total  indebtedness 
in  United  States  money  ? 

8.  What  is  the  gain   on  2500   yd.  of    English  woolens 
bought  at  3s.  6d.  per  yard,  and  sold  at  f  1.40  per  yard  ? 

9.  What  is  the  gain  in  U.S.  money  on  a  French  auto- 
mobile costing  8000  francs,  if  sold  in  England  for  £  420  ? 

10.  A  druggist  bought  200  lb.  (commercial  weight)  of 
chemicals  at  31^  per  pound.  What  is  his  gain  if  he  sells  at 
42^  per  pound  (apothecaries'  weight)  ? 

Group  5 


1.    Add  1,  f. 

Oral  Work 
*• 

2.    Multiply 
Multiply 
Multiply 
Multiply 
Multiply 

61  by  61 ;  650  by  650 
51  by  31;   5.5  by  350 
81  by  71;  .85  by  .75 
6^  by  6^  ;  625  by  625 
91  by  61;  6.33J  by  9.3^ 

Solve  : 

3.  .061-4 

4.  25^.121    5.  75X.75 

6.  60  X  31 

.125^5 

32^.25          45  X. Ill 

15^.31- 

.033^110 

48^.061         30  X. 331 

12  X  .621 

.3458^1000 

75-f-.06f         2400  X. 081 

.121^.661 

42.68 -r- 200 

.72-.08J        6400  X  .16f 

.6f  X  5 

7.  What  will  be  the  cost  of  25  bath  robes  at  12.50  each? 

8.  What  will  be  the  cost  of  15  squares  of  gravel  roofing 
at  1 1.50  per  square  ? 

9.  A  retailer  bought  '1540  worth  of  cotton  goods  at  6^^ 
per  yard,  and  sold  the  lot  at  12|-^  per  3^ard.  How  much  did 
he  make  ? 

10.    I  bought  300  articles  at  33^jzf  each,  and  sold  them  at 
50^  each.     How  much  did  I  gain? 


THE  EQUATION 


126.  If  a  four-pound 
weight  in  one  pan  of  the 
scales  exactly  balances  a 
quantity  of  sugar  in  the 
other  pan,  we  may  say 
that  in  respect  to  weight, 
the  four-pound  weiglit  is 
equal  to  the  sugar.  A  statement  that  one  quantity  is  equal 
to  another  quantity  is  called  an  equation. 

The  sign  of  equality  (  =  )  is  read  "equals." 

127.  The  equation  is  used  for  abbreviating  statements  : 
Thus,  the  question,  "  If  a  50-acre  farm  is  worth  $5000,  what 
is  1  acre  worth  ?  "  can  be  abbreviated  to  read  :  "  If  50  A.  = 
15000,  what  does  A.  equal?" 

P'urther,  the  statement  that,  "  If  50  acres  are  worth  -f  5000, 
1  acre  is  worth  l-50th  of  I?  5000,  or  |5 100,"  can  be  abbre- 
viated to  read : 

If  50  A.  =15000, 

A.  =  $^100,  value  per  acre, 
(By  dividing  by  50.) 

128.  If  50  A.  =  $5000,  what  will  100  A.  =  ? 

If  50  A.  =  $5000, 
100  A.  =  $10000. 
(By  multiplying  by  2.) 

129.  Further  illustrations  might  be  given  to  indicate  that 
any  operation  may  be  performed  on  both  sides  of  an  equa- 

88 


THE   EQUATION  89 

tion  without  destroying  its  value.     From  this  fact  we  de- 
rive the  following  important  rules : 

(a)  Dividing  both  sides  of  an  equation  by  the  same  num- 
ber does  not  alter  the  value  of  the  equation. 

(5)  Multiplying  both  sides  of  an  equation  by  the  same 
number  does  not  alter  the  value  of  the  equation. 

(tf)  Adding  the  same  number  to  both  sides  of  an  equation 
does  not  alter  the  value  of  the  equation. 

(d)  Subtracting  the  same  number  from  both  sides  of  an 
equation  does  not  alter  the  value  of  the  equation. 

(e)  Squaring  both  sides  of  an  equation  does  not  alter 
the  value  of  the  equation. 

(/)  Taking  the  square  root  of  both  sides  of  an  equation 
does  not  alter  the  valiie  of  the  equation. 

130.  If,  in  the  equation  50  A.  =15000,  the  value  of  A. 
('tlOO)  is  put  in  place  of  A.,  we  get  the  following  statement : 

50  X  1100  =  15000. 

This  process  is  called  substitution.  It  is  used  in  checking 
the  work,  and  in  the  application  of  formulas.  (See  §  147, 
page  94.) 

131.  Solution  of  problems  by  the  equation.  In  the  equa- 
tion 50  A.  =  $5000,  we  found  that  A.  =  #100,  or  we  say  tliat 
we  have  solved  the  equation  for  the  value  of  A. 

1.  Solve  for  x  in  the  equation  4  a;  =  20. 
Dividing  by  4,  -  a;  =  5. 

If  the  division  cannot  be  performed,  indicate  it  thus : 

Solve  for  x  in  the  equation  hx  =  20  (hx  means  h  times  x). 

20 
Dividing  by  5,  x=  20-^5,  or  —  • 

2.  Solve  for  x  in  the  equation  ^  a;  =  20. 
Multiplying  by  2,  a;  =  40. 


90  THE   EQUATION 

3.  Solve  for  x  in  the  equation  2  a;  +  5  =  a:  +  15. 
Subtracting  5,  2  a:  =  a:  -h  10. 
Subtracting  rr,  a;  =  10. 

4.  Solve  for  x  in  the  equation  2  a:  —  4  =  16. 
Adding  4,  2  a;  =20. 
Dividing  by  2,  a;  =  10. 
Substituting  10  for  x,  (2  x  10)  -  4  =  16  (checlz). 

Note.     Add  or  subtract  until  the  left-hand  side  of  the  equation  has 
only  the  term  containing  the  unknown. 

5.  Solve  for  x  in  the  equation  q^=\^. 
Extracting  square  root,  a;  =  4. 

6.  Solve  for  x  in  the  equation  Va:  =  3. 
Squaring,  a;  =  9. 
Solve  and  check  : 

7.  3a;  =  a:  +  10 

8.  7  a: +  10  =  5  a; +  14 

9.  Ja:=3 

10.  9a;-10=2aj  +  ll 

11.  fa:  =15 

12.  1^  =  4 

13.  If  PR  =  20,  find  n, 

14.  If  ah  —  <?,  find  h. 

15.  If  PR  =  7,  find  R, 

16.  If  Pi22^=7,  find  T. 

17.  li  PRT=l  find  R, 

18.  If  Pi2y=7,  find  P. 

19.  If  P+P72r=^  findi?. 

Suggestion.  P  +  PR  T=  A. 

Subtracting  P,  PRT  =  A  -  P. 

Dividing  by  Pr,  ^  =  ^^f^' 


THE   EQUATION  91 


20.    Ji  X  -{-  ax  =  1/^  find  x. 
Suggestion.  x  +  ax  =  y. 

Factoring,  x(l  -{-  a)  -y. 

Dividing  by  1  +  «,  x 


1  +  a 

21.  If  P  +  PRT=  A,  find  P. 

22.  If  ^  +  BRT=  A,  find  B. 

23.  If  ^  +  5i2r=7l,  findi?. 

24.  If  ^  + ^57^2^=^,  find  r. 

25.  If  ^  =  3  and^  =  12,  find  Ain  m  =  A 

Suggestion.  If  Bh  —  A, 

Substituting,  Sh  =  12. 

Then,  h  =  i. 

26.  If  A  =  4  and  A  =  16,  find  ^  in  ^Bh  =  A. 

27.  If  5=3and  A  =  4,  find  ^in^2_^  +  A2. 

28.  If  A  =  3,  A:  =  12,  ^  =  16,  and  A  =  40,  find  P  in  PA  + 
k  +  K=A. 

29.  If  ir=  15  and  F=  45,  find  h  in  J  A^=  F. 

30.  If  TT  (called  pi)  =  3.1416  and  A  =  28.2744,  find  r  in 
7rr2  =  A. 

If  a  =  3,  5  =  4,  and  c  =  5,  find  a;  in  the  following  : 

31.  x-{-a  =  c  37.  a^  +  x  =  P-\-c 

32.  2x-j-b  =  x-{-  2a  38.  x'^  =  4:  a-\-b 

33.  X  —  a  =  S  b  39.  b  =  x^ 

34.  c-\-Sx  =  Ba  —  b  40.  ax  =  be 

35.  2  a  +  4  ^  =  6  J  41.  bx  =  ac  -{-  9 

36.  a  +  b  -\-  c  =  S  x  42.  2  a:  —  10  =  abc 


MENSURATION 


132.  A  line  has  one  dimension,  length. 
Note.     Parallel  lines  have  the  same  direction. 

133.  An  angle  is  the  difference  in  direc- 
tion of  two  lines  that  meet. 


134.  If  two  lines  cross  or  meet,  one  being 
perpendicular  to  the  other,  they  form  right 
angles. 


PLANE   FIGURES 


Parallel  Lines 


Right 
Angle 


Perpendicular  Lines 


135.  A  polygon  is  a  plane  surface  bounded  by  straight 
lines.  Polygons  derive  their  names  from  the  number  of 
their  sides,  as  triangle,  quadrilateral,  etc. 

136.  A  triangle  is  a  plane  surface  having 
three  sides  and  three  angles. 

Triangle 

137.  A  right  triangle  is  a  triangle  having  a 
right  angle. 

Note.     The  side  opposite  the  right  angle  is  called 
the  hypotenuse.  Right  Triangle 

138.  A  quadrilateral  is  a  plane  surface  having  four  sides 
and  four  triangles. 


PLANE  FIGURES 


93 


Notes.     1 .   When  the  sides  are  parallel,  it  is  called  a  parallelogram. 

2.  If  the  parallelogram  has  right  angles,  it  is  called  a  rectangle. 

3.  If  a  rectangle  has  equal  sides,  it  is  called  a  square. 


Quadrilateral 


Rectangle 


Parallelogram 


Square 


j^\3^^Hl££^ 


139.  The  base  of  a  plane  figure  is  the  side  upon  which  it 
is  supposed  to  stand. 

140.  The  altitude  is  the  perpendicular  distance  from  the 
base  to  the  vertex  (highest  point  of  the  figure). 

141.  A  circle  is  a  plane  surface  bounded 
by  a  curved  line  (circumference),  every 
point  of  the  circumference  being  equally 
distant  from  the  center. 

142.  The  diameter  of  a  circle  is  a  straight 
line  drawn  through  the  center,  terminat- 
ing in  the  circumference. 

143.  The  radius  of  a  circle  is  the  distance  from  the  center 
to  the  circumference,  or  half  the  diameter. 

144.  The  perimeter  of   a   plane  surface   is   the   distance 
around  it. 

145.  The  area  of  a  plane  figure  is  the  number  of  square 
units  within  its  boundary  lines. 


94  MENSURATION 

146.  Abbreviations  used  : 

h  =  altitude. 

B  =  base. 

a,  b,  c  =  the  three  sides  of  a  triangle. 

P  =  perimeter. 

S  =:i(a-hh  +  c'). 

H         =  hypotenuse. 

C  =  circumference. 

D  =  diameter. 

r  =  radius. 

TT  (pi)  =  3.1416. 

147.  Formulas  for  plane  figures : 

1.  Parallelogram, 

B  X  h  =  area. 
(The  base  multiplied  by  the  altitude  equals  the  area.) 
To  THE  Teacher.      Require  the  pupil  to  interpret  all  the  formulas. 

2.  Triangle, 

(a)  Base  and  altitude  iDeing  given, 
B  X  I  h  =  area. 

(5)  The  three  sides  (a,  b,  c,)  being  given, 


VaS'(aS'  -  aX>S  -b){S--c)  =  area. 

Ex.    Find  the  area  of  a  triangle   if  the  three  sides  are 
15  ft.,  17  ft.,  and  18  ft. 

5  =  H15  +  17  +  18)  or  25. 


\/25  X  10  X  8  X  7=  118.3+  sq.  ft. 

(<?)  Two  sides  of  a  given  right  triangle  to  find  the  third. 
(Either  leg  may  be  considered  the  base.) 


PLANE  FIGURES  95 

(1)   H^  =  B^^W 


H  =  V^  4-  h^  (For  taking  square  root,  see  Appendix.) 

(2)  B^  =  ^2  _  7^2    (Subtracting    h^    from    both   sides  in 

the  first  equation.) 

(3)  h^=.  m-  m     (Why  ?) 

h    =  V^2_  ^2 

3.   Circle, 

2)  X  77  =  circumference. 

Q  ^  IT  —  diameter. 

^(i>  X  O  =  ^i"ea. 

7*2  X  TT  =  area. 

i>2  X  i7r(|7r  =  .7854)  =  area. 

EXERCISES 
Find  the  area  and  perimeter  of : 
1.    A  rectangle,  base  72  rd.,  width  30  rd. 
2..  A  square,  base  25  rd.,  width  25  rd. 

3.  A  rectangle,  base  30  rd.,  width  42  rd. 

4.  A  circle,  radius  3  ft. 

5.  A  circle,  diameter  4  ft. 

6.  A  circle,  circumference  24  ft. 

7.  Find  the  area  of  a  triangle  whose  sides  are  15^  16', 
and  17^ 

8.  Find  the  base  of  a  right  triangle  whose  hypotenuse  is 
10  ft.  and  one  side  6  ft. 

9.  What   is  the   hypotenuse    of   a   right  triangle  whose 
other  two  sides  are  9  ft.  and  12  ft.  ? 


96 


MENSURATION 


10.  Find  the  area  of  a  right  triangle,  if  its  base  and  per- 
pendicular are  7  ft.  and  8  ft.  respectively. 

11.  In  a  right  triangle  the  hypotenuse  is  25  fl.,  the  base 
13  ft.     What  is  its  area  ? 

12.  A  rectangular  field, is  70  rd.  long  and  has  an  area  of 
40  A.     What  is  its  width  ? 

13.  How  many  square  feet  in  the  floor  of  a  room  40  ft. 
by  20  ft.  ? 

14.  A  yard  is  75  ft.  by  165  ft.  What  will  it  cost  to  fence 
it  at  12J^  per  foot? 

15.  If  a  walk  3  ft.  wide  is  inside  the  fence  of  a  rectangular 
garden,  how  much  area  does  the  walk  cover,  the  garden 
being  30  ft.  by  40  ft.  ? 

16.  A  square  field  containing  40  A.  has  a  road  30'  wide 
running  completely  around  it  outside  the  fence.  Find  the 
area  of  the  road  in  acres  and  square  rods. 


SOLIDS 

148.  A  solid  has  three  dimensions,  —  length,  breadth,  and 
thickness. 

149.  A  prism  is  a  solid  whose  ends  or  bases 
are  any  equal,  similar,  and  parallel  plane  fig- 
ures, and  whose  lateral  faces  are  parallelo- 
grams. 

Note.     Prisms  are  named  from  the  number  of  sides      L 
forming  their  bases,  —  triangular  prisms,  quadrilateral 
prisms,  etc. 


150.   A  cube  is  a  prism  having  all  three 
dimensions  equal. 


Quadrilateral 
Prism 


Cube 


SOLIDS 


97 


151.  A  circular  cylinder  is  a  solid  having 
equal,  parallel,  circular  bases,  and  its  lateral 
surface  a  uniform  curve. 


Circular  Cylinder 


152.    A  pyramid  is  a  solid  having  a  polygon 
for  a  base  and  triangles  for  sides. 


Pyramid 


153.  A  circular  cone  is  a  solid  having  a 
circular  base,  and  lateral  surface  tapering  to 
a  point. 


Circular  Cone 

154.  The  altitude  of  a  solid  is  the  perpendicular  distance 
from  its  base  to  the  highest  point. 

155.  The  slant  height  of  a  pyramid  is  the  altitude  of  its 
triangular  lateral  surface. 

156.  The  slant  height  of  a  cone  is  the  shortest   distance 
from  the  circumference  of  its  base  to  its  vertex. 

157.  The  volume  of  a  body  is  the  number  of  cubic  units 
it  contains. 

158.  Additional  abbreviations: 

K  =  area  of  lower 
k  =  area  of  upper 
St.  ht.  =  slant  height. 

BUS.    ARITH. 7 


98  MENSURATION 

15&.  Formulas  for  solid  figures: 

1.  Pkism, 

(a)    K  X  h  =  volume. 

(6)     P  X  h=  area  of  lateral  surface. 

(c)  (F  X  h)  -\-  k  -^  K=  total  area. 

2.  Cylinder, 

(a)  Kx  A  =  volume. 

(h)   P  X  h  =  area  of  lateral  surface. 

(t?)  (P  X  A)  +  A:  -h  K=  total  area. 

3.  Pyramid, 

(a)  K X  ^h  =  volume. 

(h)  P  X  I  8t.  Jit.  =  area  of  lateral  surface. 

(c)  (P  X  I  8t.  ht.)  4-  K=  total  area. 

4.  Cone, 

(a)  K  X  I  h=  volume. 

(b)  P  X  1st.  ht.  =  area  of  lateral  surface. 

(c)  (P  X  I  8t.  ht. )  +  ir=  total  area. 

Notes.     1.    The  prism  and  cylinder  have  like  formulas. 

2.  The  pyramid  and  cone  have  like  formulas. 

3.  In  formulas  1  (c)  and  2  (c),  A'  =  k. 

EXERCISES     . 
Find  the  volume,  lateral  area,  and  total  area  of  : 

1.  A  rectanglar  prism,  sides  of  base  8  ft.  and  4  ft.,  alti- 
tude 9  ft. 

2.  A  triangular  prism,  sides  of  base  4  ft.,  altitude  9  ft. 

3.  A  cylinder,  diameter  of  base  5  in.,  altitude  10  in. 

4.  A  cylinder,  radius  of  base  2  in.,  altitude  8  in. 


SOLIDS  99 

5.  A  pyramid,  base  a  square  6  ft.  on  a  side,  altitude  4  ft., 
slant  height  5  ft. 

6.  A  cone,  diameter  of  base  4  in.,  altitude  7  in. 

7.  A  triangular  prism,  sides  of  base  4  in.,  5  in.,  and  7  in., 
altitude  11  in. 

8.  A  cube,  8  in.  on  a  side. 

9.  How  many  gallons  of  water  will  a  cylindrical  cistern 
hold  if  its  diameter  is  8  ft.  and  depth  20  ft.  ?     (See  §  110.) 

10.  The  volume  of  a  cylinder  is  500  cu.  in.,  and  its  base 
has  a  diameter  of  10  in.     What  is  its  height  ? 

11.  The  volume  of  a  prism  is  320  cu.  ft.,  and  its  base  is  a 
square,  4  ft.  on  a  side.     Find  the  altitude. 

12.  A  cylinder  25  ft.  high  has  a  capacity  of  1000  cu.  ft. 
What  is  the  diameter  of  its  base  ? 

13.  How  many  cubic  yards  of  dirt  will  it  take  to  make  a 
fill  300  yd.  long,  10  ft.  high,  and  30  ft.  wide  ? 

14.  What  must  be  the  diameter  of  a  cylindrical  gallon 
measure  7  in.  high? 

15.  A  has  a  cylindrical  cistern,  diameter  4^  depth  10'. 
What  is  the  diameter  of  B's  cistern  of  the  same  shape  and 
depth,  holding  8  times  as  much  as  A's? 

16.  The  volume  of  a  cube  each  edge  of  which  is  6"  is  how 
many  times  as  great  as  that  of  a  cube  each  edge  of  which  is  2''  ? 

17.  How  many  square  yards  of  tin  will  be  required  tc 
make  42  cylindrical  pails,  without  covers,  10^'  in  diameter 
and  12'^  deep,  allowing  4  sq.  ft.  for  seams  and  waste  on  each 
dozen  pails  ? 

18.  A  rectangular  swimming  pool  is  60  yd.  long,  80  ft. 
wide,  and  10  ft.  deep.  How  long  will  it  take  to  fill  it  with 
water  to  within  3  ft.  of  the  top,  if  the  water  runs  in  at  the 
rate  of  8  cu.  ft.  per  second  ? 


PRACTICAL   MEASUREMENTS 

160.  Papering  is  estimated  by  the  roll,  either  single  roll 
(18  ft.  long  by  18  in.  wide),  or  by  the  double  roll  (48  ft.  long 
by  18  in.  wide).  It  is  more  economical  to  use  double  rolls 
on  account  of  the  saving  in  matching  the  pattern. 

Note.     Imported  papers  vary  in  length  and  width. 

161.  Use  the  following  rules  for  estimating  the  number  of 
rolls  required  for  any  given  room  : 

1.  Deduct  the  width  of  all  openings  (doors  and  windows) 
from  the  perimeter  of  the  room.  Divide  this  result  by  the 
width  of  the  paper  to  determine  the  number  of  strips  required 
for  the  walls.  The  length  of  each  strip  will  be  the  height 
of  the  room. 

2.  Divide  the  width  of  the  ceiling  (width  of  the  room)  by 
the  width  of  the  paper  to  determine  the  number  of  strips 
required  for  the  ceiling.  Each  strip  will  be  the  length  of 
the  room. 

3.  Determine  the  number  of  strips  (of  each  kind)  that 
can  be  cut  from  a  roll,  and  divide  this  into  the  number  of 
strips  required  to  determine  the  number  of  rolls  required. 

Note.  Spaces  above  and  under  doors  and  windows  (not  allowed  for 
in  the  above  calculations)  can  usually  be  covered  with  the  strips  left 
over  in  matching  the  pattern. 

162.  Painting  and  plastering  are  estimated  by  the  square 

yard.   Make  allowance  for  openings,  unless  otherwise  directed. 
Note.     Contracts  usually  specify  allowances  for  openings. 

163.  Carpet  is  sold  by  the  linear  (running)  yard  ;  linoleum 
by  the  square  yard. 

100 


PAPERING,   PAINTING,   PLA8Tj3RtS(^      ''        tOlr 

Carpets  vary  in  width  ;  this,  as  well  as  the  matching  of 
the  pattern,  must  be  taken  into  account  in  figuring  the  number 
of  yards  necessary  for  a  given  floor.  The  strips  are  laid  the 
long  way  of  the  room. 

EXERCISES 

1.  Find  the  cost  of  plastering,  papering,  and  carpeting  a 
room  20  ft.  long,  16  ft.  wide,  and  10  ft.  high  (20'  x  W  x  10'). 
It  has  5  windows,  each  6'  x  3',  2  doors  7'  x  3^  and  1  door 
7'  X  6'.  Paper  costs  $1.12J  per  double  roll ;  plastering  costs 
40  ^  per  square  yard  ;  the  carpet  is  |  yd.  wide,  at  f  2  per  yard. 

Plastering 

Area  of  walls  =  2  x  (20  x  10)  +  2  x  (16  x  10)  =  720 
Area  of  ceiling  =  20  x  16  =  320 

Total  area  1040  sq.  ft. 

Openings : 

5  windows  =  5  x  (6  x  3)  =  90 
2  doors  =  2  X  (7  X  3)  =  42 
1  door         =7x6  =42 

174  sq.ft.  174  sq.ft. 

Area  to  be  plastered  866  sq.  ft. 

-8.|5.  =  number  of  square  yards. 

866x1.40^^  3g^^g^  ^^^^  ^^  40^  per  square  yard. 

Papering 

Perimeter  of  room  =  2  x  (20  -h  16)         =  72 
Width  of  5  windows  =  5  x  3  =  15 
Width  of  2  doors        =2x3=6 
Width  of  1  door         =  _6 

Total  width  to  be  deducted        27  ft.         27 

45  ft. 
45'  -- 18"  (I)  =  30  strips,  each  10'  long,  for  the  walls. 
16'  -^  I'  =  10|  or  11  strips,  each  20'  long,  for  the  ceiling. 


'162.':  •;    .  -.  JPI^ACTICAL  MEASUREMENTS 

As  each  roll  is  48'  long,  4  ten-foot  strips  or  2  twenty-foot 
strips  can  be  cut  from  each  roll. 

Hence,  30  -f-  4  =  7|-,  or  8  rolls  for  the  walls. 

11-f-  2  =  5 J,  or  6  rolls  for  the  ceiling. 
Total  required  is  8  -f  6  or  14  rolls. 
14x1 1.121-  =  '*  15.75. 

Carpeting 

As  the  room  is  16'  wide,  as  many  strips  of  carpet  will  be 

required  as  |  yd.  (the  width  of  the  carpet)  is  contained  in  16'. 

I  yd.  =  21'.     16  -5-  21  =  71  or  8  strips,  each  20'  long. 

20  X  8 
20  X  8  =  number  oifeet;  ^^— - — -  =  number  of  yard%» 

o 

2.  At  20  j^  per  square  yard,  how  much  will  it  cost  to  plaster 
the  walls  and  ceiling  of  a  room  18'  x  15'  x  7'  4",  making  allow- 
ance for  2  doors  7'  6"  x  8'  6",  and  3  windows  6J'  x  3'? 

3.  A  room  is  15'  x  12'  x  9'.  How  much  will  it  cost  to 
paper  it  at  37 J  ^  per  double  roll,  allowing  for  2  doors  8'  x  4' 
and  for  2  windows  6'  4"  x  3'  3"  ? 

4.  A  wall  is  16'  long  and  12'  high.  How  many  double 
rolls  of  paper  will  it  take  to  paper  it,  no  allowance  being 
made  for  openings  ? 

5.  A  barn  is  100' x  60' x  30', 
with  gables  20'  above  the  walls. 
If  no  allowance  is  made  for 
openings,  what  will  it  cost  to 
paint  it  at  5  ^  per  square  yard  ? 

6.  How  many  yards  of  carpet  1  yd.  wide  will  it  take  to 
cover  a  room  14'  x  10',  strips  running  lengthwise  ? 

7.  How  many  yards  of.  carpet  |  yd.  wide  will  it  take 
to  cover  the  library,  dining  room,  and  living  room,  in  the 


100' 


ROOFING  AND  FLOORING 


103 


v//////. 


KLTCHEN 

io'-irxi3-r 


LIBRARY 

12-7"  X  15-3" 


fir 


DININQ  PsO^M 
I6'-7"X  13-2" 


■3) 


II    LIVING  RO^M  I 


I2-7"XI2-H" 


/ 
/ 


HALL 

7- 3' XI 7-0" 

i      i 


-r////////(i>=p       u=^///////}- 


■^//////A 


accompanying  floor  plan,  no  allowance  being  made  for  match- 
ing patterns  ? 

8.  How  many  yards  of  linoleum  will  it  take  to  cover  the 
kitchen  ? 

9.  How  much  will  the  carpet  in  problem  7  cost  at  il.33 
per  yard  ? 

164.  Roofing  and  flooring  are  usually  measured  by  the 
square  of  100  square  feet.  Flooring  is  sometimes  measured 
by  the  1000  board  feet. 

165.  The  most  common  roofing  materials  are  :  slate,  tiling, 
shingles,  and  tin. 

The  size  of  slate  used  is  generally  12"  x  6^  or  24"  x  16^ 

Note.  Contractors  use  a  table  for  estimating  the  amount  of  slate  to 
be  used. 

The  size  of  shingles  used  is  generally  16"  x  4",  or  18"  x  4". 
16"  x  4"  shingles  are  laid  with  4"  exposed  to  the  weather. 


104  PRACTICAL  MEASUREMENTS 

166.  Shingles  are  sold  in  bundles  of  250  each.  Allowing 
for  waste,  the  usual  estimate  of  the  number  of  shingles  per 
square  is  shown  in  the  following  table. 


Pakt  exposed 

Number  Shingles 

TO  THE  Weather 

PER   SyllARE 

4  " 

1000 

H" 

900 

5  " 

800 

5A" 

700 

Ex.     A  gable  roof  is  40'  long  and  20'  on  each  side.     How 
many  shingles  laid  -i"  to  the  weather  must  be  bought  to 
cover  it  ? 
4        2 

iPx^^x2  ^  ^Q  squares,     length  x  width  x  no.  sides 
lipp  *      no.  square  ft.  in  a  square 

16  X  1000  =  16000  shingles  (by  table). 

167.  In  flooring,  a  waste  of  about  ^  of  the  total  amount  of 
lumber  required  is  allowed  for  the  "tongue  and  groove." 

Use  cancellation  when  possible  : 

1.  I  wish  to  floor  a  room  20'  x  16'.  How  much  will  the 
material  cost  at  fSO  per  thousand  square  feet? 

2.  How  many  bundles  of  shingles  16"  x  4"  will  be  re- 
quired to  cover  a  roof  120'  x  40'  ? 

3.  At  $4:  per  thousand  how  much  will  it  cost  to  shingle  a 
roof  100'  X  80',  allowing  800  shingles  to  the  square  ? 

4.  Find  the  cost,  at  i40  per  thousand  square  feet,  of  the 
tongued  and  grooved  flooring  for  a  room  30'  x  20'. 

168.  Lumber  is  sold  by  the  1000  (M)  board  feet.  A  board 
foot  is  1  ft.  long,  1  ft.  wide,  and  1  in.  thick. 

Note.     Boards  less  than  1"  thick  are  counted  as  1"  thick. 

169.  In  making  extensions  in  bills  of  lumber,  point  off  3 
places  and  multiply  by  the  price  per  1000  feet,  using  aliquot 
parts  and  cancellation. 


WOOD,   STONE,   BRICKS  105 

At  $22  per  M  what  is  the  cost  of  60  pieces  of  hemlock 
16' X  6"  x2''? 

5 

16  X  6  X  2  X  ^j3  X  22  ^  ^  21  1^  Divide  by  12  because  the  width 

12  '   *^      is  expressed  in  inches. 

Make  the  extensions  in  the  following  bill  of  lumber : 


200  pieces  18'  x  12"  x  2" ft. 

500  pieces  14'  x  10"  x  3"           ft. 

150  pieces  16'  x  15"  x  2" ft. 

250  pieces  12'  x    8"  x  2" ft. 

400  pieces  16' X    2'    x  4" ft. 

1000  pieces  16'  x    4"  x  2" ft. 

Total    ft.  @  $.33.00  per  M   .... 

600  running  feet  2"  x  4"               @    33.33  per  M   .     .     .     . 

15000  board  feet  oak  flooring            @    35.00  per  M   .     .     .     . 

20  M  shingles                                 (oj      4.  .50  per  M   .     .     .     . 

Total 

170.  Wood  is  measured  by  the  cord.     A  cord  of  wood  is 
8  ft.  long,  4  ft.  wide,  and  4  ft.  high,  and  contains  128  cu.  ft. 

Note.     A  cord  foot  is  1  ft.  of  the  length  of  such  a  pile. 

Use  cancellation  : 

1.  How  many  cords  of  wood  in  a  pile  40'  x  20'  x  8'  ? 

2.  At  15  per  cord,  how  much  will  it  cost  to  fill  with  wood 
a  shed  25'  x  15' x  18'? 

171.  Stone  is  measured  by  the  cubic  yard,  or  by  the  perch 
(24|cu.  ft.). 

172.  Bricks  are  estimated  by  the  M.     22  common  bricks 
laid  in  mortar  are  counted  for  each  cubic  foot  of  wall. 

Note.     Allowance  is  always  made  for  openings  in  ordering  material 
and  in  making  contracts. 


106  PRACTICAL  MEASUREMENTS 

SPECIAL   METHODS 

173.  To  find  the  number  of  bricks  in  a  wall,  multiply  the 
number  of  cubic  feet  in  the  wall  by  22. 

174.  To  find  the  number  of  perches  of  stone,  in  a  wall, 
divide  the  number  of  cubic  feet  in  the  wall  by  24J. 

1.  How  many  perches  of  stone  in  a  wall  15'  x  8'  x  8'  ? 

2.  How  many  bricks  will  be  required  to  erect  the  four 
walls  of  a  flat  building  60'  x  40'  x  20',  an  allowance  of  200 
cu.  ft.  being  made  for  the  openings  and  corners,  and  the 
walls  being  12"  thick  ?• 

DIFFERENCES   IN   TIME 

175.  Two  methods  are  employed  in  finding  the  difference 
in  time  between  two  dates : 

1.  Exact  number  of  days. 

P'ind  the  exact  number  of  days  from  Feb.  2, 1912,  to  June  4, 

1912 

29,  number  days  in  February 

27,  number  days  left  in  February 
31,  number  days  in  March 

30,  number  days  in  April 

31,  number  days  in  May 
4,  number  days  in  June 

123  da. 

2.  Compound  subtraction. 

What  is  the  difference  in  time  between  Oct.  24,  1909,  and 
May  8,  1911  ? 

Ye.         Mo.       Da. 

1911        5        8  May  is  the  5th  month  in  the  year,  October  the 

1909      10      24       10th  month.     The  subtraction   is  performed  by  the 

1        6      14      method  of  denominate  numbers.      (1  mo.  =  30  days) 


APPLICATION  TO  MANUAL  TRAINING  107 

Find  the  difference  in  time  between  the  following  dates : 

3.  From  Jan.  23  to  Nov.  15  of  the  same  year.  (Not  a 
leap  year.) 

4.  From  Dec.  13,  1910,  to  April  3,  1912.  (Compound 
subtraction.) 

5.  From  May  10,  1900,  to  Jan.  5,  1904.  (Compound 
subtraction.) 

6.  From  Jan.  1,  1913,  to  Dec.  25,  1913. 

APPROXIMATIONS   USED    IN   BUSINESS 

176.  To  find  the  number  of  bushels  of  grain  in  a  bin, 
multiply  the  capacity  in  cubic  feet  by  .8. 

177.  To  find  the  number  of  heaped  bushels  of  fruit  or 
vegetables  in  a  bin,  multiply  the  capacity  in  cubic  feet  by  .63. 

178.  To  find  the  number  of  gallons  in  a  cistern  or  reser- 
voir, multiply  the  capacity  in  cubic  feet  by  7.48. 

Find  the  approximate  number  of  bushels  of  (a)  grain, 
(6)  apples,  in  the  following  bins: 

1.  12^  X  10'  X  8'  3.    16'  X  8'  4"  x  7' 

2.  20'  X  15'  X  10'  4.    18'  3"  X  15'  9"  x  12'  4" 
Find  the  approximate  number  of  gallons  in  the  following: 

5.  A  cylindrical  cistern,  diameter  4',  depth  20'. 

6.  A  cylindrical  cistern,  radius  3',  depth  15'. 

7.  A  reservoir,  100  rd.  x  60  rd.  x  50'. 

APPLICATION  OF  PRACTICAL  MEASUREMENTS  TO 
MANUAL  TRAINING 

1.  A  room  32'  x  28'  is  laid  off  so  as  to  accommodate  20 
pupils  in  manual  training.  Allowing  one  fifth  of  the  floor 
space  for  the  teacher's  use  in  demonstration  work,  how  much 
floor  space  is  allowed  per  pupil  ? 


108 


PRACTICAL  MEASUREMENTS 


2.    Find  the  total  cost  of  the  following  manual  training 
tools  and  supplies : 

Articlb  Pkiot 

4  augur  bits  \",  \",  f",  1''    .     .      .75 

1  mallet 36 

4  clamps 8.00 

Material  for  bench 6.00 

Miscellaneous 8.66 


Article 

Peiob 

1  block  plane  . 

$1.60 

1  jack  plane     . 

1.60 

1  rip  saw     .     . 

1.60 

1  mortise  saw  . 

1.00 

1  brace  .     .     . 

.76 

3.  At  18  ^  per  board  foot, 
what  will  poplar  lumber  f 
thick  cost  for  making  the  nail 
box  shown  in  the  illustration  ? 


4.  What  will  the  material 
cost  for  making  the  bread 
board  shown  in  the  illustra- 
tion, using  white  pine  f  thick, 
at  22  ^  per  board  foot  ?  Add 
expense  of  sanding  at  2^  per 
board  foot. 


^^' 


5.  At  26  ^  per  board  foot,  what  will  the  material  cost  for 
making  the  table  shown  in  the  illustration?  Add  expense 
of  sanding  at  2  ^  per  board  foot  for  all  lumber  used. 


MISCELLANEOUS  PROBLEMS 


109 


6.  Find  the  cost  of  material  and  sanding  in  the  following, 
quartered  oak  being  26  ^  per  board  foot,  and  pine  and  bass- 
wood  being  32  ^ ;  sanding  is  2  ^^  per  board  foot. 


MANUAL  TRAINING  MILL  BILL 

Order  No 

School    H.  S.  of  Commerce  Date  12/4/13 

Name    Walter  Burkholz  Gut  by 

Project    Music  Cabinet  Delivered 

Ordered  by    W.  B.  Cutter 


Kind  of  Wood 


Quartered  oak 

Pine 
Bass 

All  sanded 


Thickness      Width       Length 


1" 
1" 
1" 

I" 
f" 


18" 
16" 
17" 
24" 


21" 
38" 
28" 
24" 
17" 


Article 


Top 
Sides 
Door 

Shelves 


MISCELLANEOUS   PROBLEMS 
Group  1 

1.  Find  I  in  the  equation  1=  FET,  if  P  =  |300,  i^  = 
.06,  and  T=  {. 

2.  Find  R  in  the  equation  PBT=  J,  if  P  =  1250,  T=  |, 
and  7=  $6.25. 

3.  Solve  for  A  in  the  equation  A  =  9  tt. 

4.  Find  the  area  of  a  circle  whose  radius  is  3. 

5.  Solve  for  c  in  the  equation  <?  =  2  r,  if  r  =  11  J. 

6.  Find  the  circumference  of  a  circle  whose  radius  is  94. 


110 


PRACTICAL  MEASUREMENTS 


2.^  !  ^X  7.    A  race  track  is  laid  out 

as   shown   in   the   figure,   the 
ends  being  semicircles  with  a 
diameter  x.    The  sides  are  2  x 
in  length.     How  long  is  the  track  if  a:  =  184.83  ft.? 

8.  Solve  for  A  in  the  equation  A=  Qa^^  (1)  if  a  =  2  ; 
(2)  if  a=l;   (3)  if  fl  =  .l. 

9.  Find  the  total  area  of  a  cube  (1)  whose  edge  is  2 ; 
(2)  whose  edge  is  1  ;   (3)  whose  edge  is  .1. 

10.    Solve  for  x  in  the  equation  x=1a^^  if  a  =  90  ft. 


Group  2 

1.  A  baseball  diamond  is  a 
square  90  ft.  on  a  side.  How 
far  is  it  from  home  base  to 
second  base  ? 

2.  The  diameter  of  an  auto- 
mobile tire  is  30'^  How  many 
times  does  the  wheel  turn  in 
going  ^  of  a  mile  ? 

3.  Two  buildings,  separated 
by  an  alley  15'  wide,  are  103  and 
78  ft.  high,  respectively.     How  far  is  it  from  tlie  roof  of 
the  taller  building  to  the  roof  of  the  lower? 

4.  How  many  30''  steps  must  be  taken  in  walking 
diagonally  across  a  square  40-A.  field  ? 

5.  How  long  a  rope  will  it  take  to  reach  from  the  top  of  a 
30-ft.  derrick  to  a  point  on  the  ground  18  ft.  from  its  base  ? 

6.  A  cogwheel  railroad  gains  in  elevation  1000  ft.  in 
1  mi.  of  track.  What  horizontal  distance  has  been  covered, 
the  track  being  straight  ? 


MISCELLANEOUS  PROBLEMS  111 

7.  A  railroad  track  describes  a  semicircle  around  the 
base  of  the  mountain  on  a  radius  of  2200  ft.  How  much 
longer  is  the  curve  than  a  tunnel  straight  through  would 
have  been  ? 

8.  How  many  gallons  of  oil  can  be  stored  in  a  cylindrical 
tank  40'  in  diameter  and  30'  high? 

9.  How  many  cubic  feet  of  water  would  cover  an  acre  of 
ground  to  a  depth  of  1  in.  ? 

10.  What  is  the  depth  of  a  cylindrical  quart  measure  4^" 
in  diameter  ? 

Group  3 

1.  At  'f  1.28  a  yard,  how  much  will  it  cost  to  carpet  a 
room  18'  x  16'  with  Brussels  carpet  J  of  a  yard  wide? 

2.  How  much  will  it  cost  to  dig  a  cellar  30'  xl6'  x  9'  4", 
at  33 J  ^  per  cubic  yard  ? 

3.  A  grocer  bought  a  36-gal.  barrel  of  cider  for  §5.40, 
and  retailed  it  so  as  to  gain  !i5l.80.  How  much  did  he  receive 
per  quart  ? 

4.  What  would  be  the  cost  of  a  hardwood  floor  2"  thick 
in  a  room  18'  x  16'  4",  if  the  lumber  costs  133^  per  M,  and 
labor  costs  112.75? 

5.  How  much  will  it  cost  to  paper  a  room  20'  x  18'  x  10', 
allowing  for  2  windows  each  5'  4"  x  3'  6"  and  for  1  double 
door  8'  X  6',  if  the  paper  costs  60^  per  double  roll  ? 

6.  At  32^  per  square  yard,  how  much  will  it  cost  to 
plaster  the  walls  and  ceilings  in  the  following  dwelling  : 

Library,  14'  6"  x  13'  ;  sitting  room,  14'  x  14'  ;  dining 
room,  14'  x  10';  kitchen,  12'  x  8'  6";  pantry,  6'  x  4';  3  bed- 
rooms, respectively,  14'  6"  x  13',  14'  x  12'  and  10'  x  10';  a 
hall,  22' 6"  X  4' 6"?  All  ceilings  are  9'  high.  Allow  600 
sq.  ft.  for  openings. 


112  PRACTICAL  MEASUREMENTS 

7.  How  much  will  it  cost  to  carpet  the  library,  sitting  room, 
and  dining  room  in  problem  6  with  carpet  1  yd.  wide  costing 
^1.12|  per  yard?     (No  allowance  for  matching  patterns.) 

8.  How  much  will  it  cost  to  cover  the  kitchen  and  pantry 
in  problem  6  with  72"  linoleum,  making  no  allowance  for 
matching  patterns,  at  90  ^  per  linear  yard  ? 

9.  How  much  will  it  cost  to  cover  the  bedrooms  in  prob- 
lem 6  with  plain  matting  21"  wide  at  25^  per  yard,  and  to 
lay  a  36''  runner  in  the  hall  at  85  ^  per  yard  ? 

10.    How  much  will  it  cost  to  floor  a  drill  hall  80'  x  65' 
with  1'^  hardwood  lumber  at  #35  per  M  ?     (§  168.) 

Group  4 

1.  A  man  owned  the  S  |  of  N  W  ^  of  a  section  of  land. 
He  bought  the  NW  J  of  the  N  W  ^  of  the  same  section.  How 
many  acres  did  he  then  have  ?  Draw  a  diagram  showing 
the  location  of  the  land. 

2.  A  river  falls  765  ft.  in  a  distance  of  35  mi.  What  is 
its  fall  per  mile  ? 

3.  How  many  gallons  of  water  will  be  contained  in  a 
cylindrical  standpipe  22'  in  diameter  and  72'  high  ? 

4.  Find  the  floor  space  in  a  six-story  building  which  is 
80'  X  30',  allowing  a  space  15'  x  8'  on  each  floor  for  elevators, 
and  a  space  10'  x  4^'  on  each  floor  for  stairways. 

5.  How  many  cubic  yards  of  material  must  be  moved  to 
excavate  a  tunnel  8'  square  and  ^  mi.  long  ? 

6.  Find  the  approximate  number  of  bushels  of  apples  that 
can  be  loaded  into  a  wagon  bed  9'  x  3'  4"  x  32".  (See 
§  177.) 

7.  Find  the  approximate  number  of  bushels  of  wheat  that 
can  be  stored  in  a  granary  10'  4"  x  6'  x  7'. 


MISCELLANEOUS  PROBLEMS  113 

8.  A  cylindrical  water  tank  10'  in  diameter  contains 
10575  gal.     Find  its  height.     (See  §  178.) 

9.  A  field  1320'  x  660'  is  planted  to  orchard.  The  rows 
running  the  long  way  of  the  field  are  16'  apart,  the  first 
and  last  rows  being  18'  from  the  fence;  the  trees  are  321' 
apart  in  the  rows,  the  outside  trees  being  26.25'  from  the 
fence.  How  many  trees  are  planted  to  the  acre  ?  (Make 
diagram.) 

10.  A  vessel  carries  600  T.  of  wheat  to  Liverpool,  where 
it  is  sold  at  3s.  Ibd.  per  bushel.  What  is  the  value  of  the 
cargo  in  United  States  money  ? 

Group  5 

The  following  problems  are  to  be  solved  with  the  aid  of  the 
illustration  on  the  following  page: 

Data 

Total  length 100' 

Total  width 60' 

Height 

bottom  of  sill  to  top  of  ridge  board    .     .     .     .     .  4.0' 

bottom  of  sill  to  top  of  plate 18' 

Length 

outside  struts 18' 

inside  struts 16' 

long  members  of  trusses 11' 

short  members  of  trusses 8' 

Distance  between  struts  lengthwise  of  barn 18'  except 

middle  section,  which  is 22' 

Rafters 

over  struts  6"  x  6" 12   in  number 

all  others  6"  x  2" 70   in  number 

Overhang  and  extension  of  roof 18" 

Braces  at  top  and  foot  of  struts  6"  x  4"    .     .     .     •     .     .  4'-  6"  long 

Sheathing  for  roof  has  80  rows  of  boards  4"  wide  and  |"  thick. 

Extension  of  ridge  board,  18"  on  each  end. 

BUS.    ARITH. — 8 


(114) 


MISCELLANEOUS  PROBLEMS 


115 


1.    Fill  in    tlie    number   of   pieces   of    each    kind   in    the 
following : 


Kind 


NUMBEK 


Struts  18'  long 
Struts  16'  long 
Stringers  28|'  long 
Stringers  18'  long. 
Trusses  11'  long    . 
Trusses  8'  long 
Braces  4'  6"  long  . 
Rafters  G"  x  2"    . 
Rafters  6"  xG"    . 


2.  If  no  allowance  is  made  for  corners,  how  many  linear 
feet  of  each  of  the  following  will  be  needed :  sills,  plates, 
purlins,  ridge  board  ? 

3.  What  is  the  length  of  the  rafters,  if  18'^  is  allowed  for 
the  overhang?     (See  §  147,  2  <?.) 

4.  Fill  in  the  following,  using  the  table  in  example  1 : 


•LiNKAR   FeKT 

Size 

BoABn  Feet 

Bemarks 

Sills 

320 

12  X  12 

3840 

No  allowance 

Struts 

for  corners 

Stringers    .... 
Trusses 

Braces 

Rafters 

6x6 

Ridge  board   .     .     . 
Plates    

Roof  sheathing   .     . 

Purlins 

Rafters 

6x2 

116  PRACTICAL  MEASUREMENTS 

5.  How  many  board  feet  of  flooring  will  be  used  ?  How 
many  board  feet  of  plank  ?  (No  allowance  for  anything  but 
sills.) 

6.  If  no  allowance  is  made  for  openings,  how  many  board 
feet  of  I''  lumber  will  be  used  for  siding?  (For  area  of 
gable  ends,  see  §  147^  2  a.) 

7.  If  no  allowance  is  made  for  openings,  how  many  board 
feet  of  I"  lumber  will  be  needed  for  the  four  sides  and  top 
of  the  granary?     (Granary  38'  x  29'  x  16'.) 

8.  Allowing  for  extension  and  overhang,  find  the  area  of 
the  roof. 

9.  How  many  shingles  laid  5 J"  to  the  weather  will  be 
needed  ? 

10.    Using  all  previous  data,  fill  in  and  extend  the  follow- 
ing : 

Board  Feet 
Sills 
Stmts 
Stringers 
Trusses 

Rafters  « 

Braces 
Plates 

Ridge  board 
Plank  flooring 
Purlins 

Total board  feet  @  835.00 

Flooring board  feet  @  32.00 

Siding board  feet  @  27.50 

Sheathing board  feet  @  25.00 

Granary  material board  feet  @  26.00 

M  shingles,  per  M 5.50 

Total 


PERCENTAGE 

179.  Percentage  (per  cent  =  by  the  hundred)  is  a  com- 
mercial method  of  computing  a  fractional  part,  when  that 
fractional  part  is  hundredths. 

180.  The  sign  (%)  per  cent,  or  the  decimal  fraction  show- 
ing hundredths,  as  .25  (25%),  is  used. 

181.  The  table  of  aliquot  parts  on  page  47  will  be  used 
for  most  percentage  operations;  e.g.^  12|  %  or  .12|  of  a  num- 
ber is  \  of  it. 

To  THE  Teacher.  Review  the  table  of  aliquot  parts  until  the  stu- 
dent can  recognize  all  equivalents  instantly. 

182.  The  base  is  the  number  upon  which  the  percentage  is 
computed;  e.g.^  interest  is  figured  on  the  principal  as  the 
base;  income  upon  the  investment ;  etc. 

183.  The  rate,  or  rate  per  cent,  is  a  fractional  part  of  the 
base  to  be  taken. 

184.  The  percentage  is  the  result  obtained  by  multiplying 
the  base  by  the  rate. 

185.  The  amoimt  is  the  sum  of  the  base  and  the  percen- 
tage; e.g.^  principal  plus  interest  equals  amount,  etc. 

186.  The  difference  is  the  remainder  when  the  percentage 
is  subtracted  from  the  base;  e.g,^  cost  minus  loss  equals  sell- 
ing price  (remainder). 

Note.  When  the  rate  is  a  fractional  part  of  1%,  as  .0075  (f%),  find 
1  %,  then  take  the  fractional  part  of  it. 

117 


118  PERCENTAGE 

EXERCISES 

1.    What  is  25  %  of  200  ?         2.    Find  2|  %  of  90. 

^  of  200  =  50.  21%  is  I  of  10%. 

10%  of  90  =  9. 

-Jof9  =  2J. 
Find  by  inspection: 

3.  50%  of  360  10.  40%  of  43 

4.  121%  of  24  11.  3j%of  60 

5.  25%  of  60  12.  1J%  of  120 

6.  20%  of  75  '  13.  1|%  of  360 

7.  9^5-%  of  36  14.  2J%  of  280 

8.  37|  %  of  32  15.  16f  %  of  300 

9.  331%  of  42  16.  1%  of  870 

187.   Formulas: 

Base  X  rate  =  percentage,   or   BR  =  P, 

Percentage  -^  base  =  rate,  or  —  =  72. 

JS 

Percentage  -f-  rate  =  base,  or  —  =  B. 

R 

Base  -f-  percentage  =  amount,      or  B  +  P  =  A. 
Base  —  percentage  =  difference,  or  B  —  P  =  D. 

EXERCISES 
1.    Percentage  is  400,  base  1600,  find  rate. 


2.    Percentage  is  300,  rate  20  %,  find  base. 
300-1  =  1500,  base. 


PERCENTAGE 


119 


3.  A  man  bought  a  house  for  §5000  and  sold  it  for  f  4000. 
What  was  his  rate  of  loss  ? 

15000  -  $4000  =  f  1000  loss. 

4.  If  I  sell  a  house  for  13200,  thereby  losing  20%  of  the 
cost,  how  much  did  the  house  cost? 

1  =  loss.     Then  ^  =  selling  price. 
^  is  I  of  |.     Then  I  lost  |  of  the  selling  price. 
4)3200 
800 
4000  =  cost. 

5.  Find  17  %  of  360. 

360 

17 

- —  Since  17%  is  not  a  convenient  fractional  part  of  100%,  mul- 

2520 

op  A         tiply  the  base  by  .17. 


61.20 


Find  the  missing  parts  (by  inspection  when  possible) 


Base 

Eate 

Percentage 

6. 

2400 

25 



7. 

1600 

20 

— 

8. 

2500 

— 

500 

9. 

8000 

— 

1000 

10. 

6600 

— 

2200 

11. 

— 

12i 

3000 

12. 

— 

441 

1200 

13. 

30000 

1000 

14. 

— 

12i 

5000 

120 


PERCENTAGE 


Base 

Percentaok 

Amount 

DiFFEKKNCE 

Rate  % 

15. 

2000 

_■ 

2400 

_ 

_ 

16. 

— 

1000 

6000 



— 

17. 

3000 

— 

— 



33i 

18. 

— 

— 

4400 



10 

19. 

— 

— 

6000 



381 

20. 

8000 

— 



2000 

21. 

— 

— 

14000 

— 

^ 

22. 

_ 

— 

20000 

— 

16| 

23. 

— 

— 

— 

200 

in 

24. 

— 

1000 

— 

— 

»A 

25.  A  man  bought  a  house  for  $6000.  At  what  price 
must  he  sell  it  to  gain  20  %  of  the  cost  ? 

26.  The  population  of  Omaha  according  to  the  1910  census 
is  124096,  a  growth  of  21  %  since  the  1900  census.  What 
was  its  population  in  1900  ? 

27.  A  stock  of  goods  .damaged  by  fire  sold  at  40%  less 
than  cost.  If  the  sale  amounted  to  $24648,  what  was  the 
cost  ? 

28.  If  45  gal.  of  pure  vinegar  and  5  gal.  of  water  were 
mixed,  what  per  cent  of  the  whole  was  pure  vinegar  ? 

29.  A  grocer  mixed  20  lb.  of  nuts  at  10^  per  pound  with 
30  lb.  of  nuts  at  15^  per  pound.  At  what  price  per  pound 
must  he  sell  the  mixture  to  gain  20  %  on  the  cost  ? 


GAIN   AND   LOSS 

188.   The  gross  cost  is  the  original  cost  plus  all  expenses. 

Note.     Such  expenses  might  be  freight,  cartage,  import  duties,  in- 
terest on  investment  to  time  of  sale,  insurance,  etc. 

*   189.   The  net  cost  is  the  original  cost. 


GAIN  AND   LOSS  121 

190.  The  net  selling  price  is.  the  total  selling  price  less  all 
expenses. 

Note.     Such  expenses  might  be  advertising,  soliciting,  discounts  for 
cash,  cost  of  collecting,  commissions,  storage,  etc. 

191.  In  gain  and  loss  : 

Cost  =  base. 
Per  cent  of  gain  or  loss  =  rate. 

Gain  or  loss  =  percentage. 
Selling  price  =  amount  or  difference. 

192.  Formulas : 

Cost  X  rate''=  gain  or  loss,  or  BR  =  P. 

P 

Gain  or  loss  -^  rate  =  cost,  or     —  =  jB. 

M 
p 

Gain  or  loss  -^  cost  =  rate,  or     ——  R. 

Cost  X  (100  %  -h  rate  of  gain)  =  selling  price. 
Cost  X  (100  %  —  rate  of  loss)  =  selling  price. 
Selling  price  -j-  (100  %  +  rate  of  gain)  =  cost. 
Selling  price  -¥■  (100  %  —  rate  of  loss)  =  cost. 


EXERCISES 

1.  If  a  man  lost  16%  on  his  investment  by  selling  a 
house  for  $5000,  how  much  did  the  house  cost  him? 

Selling  price  -^  (100  %  —  rate  of  loss)  =  cost. 

15952.38,  cost 
j84)5000|00. 

Note.  This  method  is  used  when  the  per  cent  is  not  an  aliquot 
part  easily  handled. 

2.  Store  fixtures  costing  #250  were  inventoried  at  the 
end  of  the  first  year  at  8J  %  below  cost.  How  much  was  the 
loss? 


122 


PERCENTAGE 


3.  I  sold  an  80-A.  farm  at  an  advance  of  20%,  thereby 
gaining  $1000.     Find  the  cost  per  acre. 

4.  A  merchant  marks  goods  25%  above  cost.  What  is 
the  cost  of  an  article  marked  at  $  30  ? 

5.  During  the  first  and  second  years  a  manufacturer 
realized  gains  of  10%  and  20%  on  his  original  investment. 
During  the  third  year  he  lost  ilOOO,  which  was  20  %  of  his 
original  capital.  How  much  did  he  gain  the  first  year  ?  The 
second  year  ? 

6.  If  coffee  loses  5  %  of  its  weight  in  roasting,  how 
much  green  coffee  will  be  required  to  produce  1000  lb.  of 
roasted  coffee  ? 

7.  A  merchant  sold  a  consignment  of  No.  3  wheat  with 
the  understanding  that  he  was  to  receive  12|  %  of  the  pro- 
ceeds. He  remitted  f  5680  for  6000  bu.  How  much  per 
bushel  did  he  receive? 

8.  I  paid  8550.50  freight  on  an  invoice  of  goods.  Later 
I  sold  the  goods  at  a  profit  of  10%  on  the  entire  cost,  receiv- 
ing $15,695.25.     What  was  the  first  cost? 

9.  On  January  1  you  begin  business,  investing  $10000 
cash.  One  year  later  your  resources  and  liabilities  are  as 
follows  : 


Rbsoi'rcbs 

LlABIMTIBS 

Cash  on  hand    .     . 

§5000 

Acc"ts  payable  .     . 

$1200  • 

Merchandise     .     . 

1500 

Notes  payable  .     . 

2000 

Keal  estate  .     .     . 

COCO 

OflBce  fixtures   .     . 

480 

Acc'ts  receivable  . 

2000 

Find  your  per  cent  of  gain  or  loss,  based  on  the  invest- 
ment. 


COMMERCIAL  DISCOUNT 


123 


10.  A  merchant  failed  in  business.  The  assignee  found 
assets  to  the  amount  of  $20000,  which  would  pay  70^  on 
the  dollar.      What  was  the  amount  of  his  indebtedness  ? 

11.  A  bank  with  deposits  of  1^875000  was  closed  by  the 
bank  examiner.  Assets  of  1750000  were  found.  What 
per  cent  of  his  money  did  each  depositor  receive? 

12.  I  sold  a  customer  goods  at  a  profit  of  20%  of  the  cost, 
but  succeeded  in  collecting  only  80  (^  on  the  dollar.  What 
per  cent  did  I  gain  or  lose  ? 

13.  A  sold  goods  to  B,  collecting  only  75  %  of  the  bill. 
If  A  came  out  even  on  the  deal,  what  rate  of  profit,  based  on 
the  cost,  had  he  added  to  the  cost  before  selling  ? 

14.  A  man  buys  a  quarter  section  of  land  for  18500,  and 
sells  it  in  20-A.  farms  at  an  average  of  162  per  acre. 
What  per  cent  of  the  cost  did  he  gain  ? 

15.  Three  cement  plants  are  operated  by  a  company.  The 
annual  report  for  1913  shows  the  cost  of  manufacture,  selling 
price,  and  output  of  each  plant.  What  per  cent  of  profit 
per  barrel  does  each  plant  make  on  the  cost  of  manufacture, 
and  what  per  cent  of  the  total  annual  profit  does  each  plant 
produce  ? 


Plant 

Cost  per  Bul. 

Ski.ling  Price 
i-ER  Bbl. 

1913 
Output 

Annual 
Profit 

A 

$1.10 
1.00 

.80 

12.20 
1.75 
1.50 

200000  bbl. 
500000  bbl.  ■ 
1200000  bbl. 

B 

C 

Total.     .... 

COMMERCIAL    DISCOUNT 

193.  Merchandise  is  usually  advertised  by  manufacturers 
at  list  price  or  catalogue  price,  from  which  the  dealers  and 
jobbers   get   certain    discounts,    known   as   trade   discounts. 


124  PERCENTAGE 

These  discounts  vary  on  different  kinds  of  merchandise 'and 
according  to  quantities  purchased. 

194.  Deduction  of  the  trade  discount  from  the  list  price 
gives  tlie  net  wholesale  price. 

NoTK.  Many  firms  which  sell  at  wholesale  only,  quote  a  net  whole- 
sale price  instead  of  the  list  price  and  trade  discount. 

195.  Wholesale  dealers  and  jobbers  buy  direct  from  manu- 
facturers at  a  discount  from  the  net  wholesale  price  because 
they  buy  in  large  quantities.  As  a  result,  a  series  of  dis- 
counts from  the  list  or  catalogue  price  occurs;  in  this  case 
the  first  trade  discount  of  a  series  is  taken  from  the  list 
price,  the  next  is  a  discount  off  the  remainder,  etc.  After 
all  discounts  are  taken,  the  remainder  is  the  net  price. 

136.  Payment  is  made  in  accordance  with  conditions  speci- 
fied at  the  time  of  sale,  known  as  terms,  which  usually  require 
payment  of  the  net  amount  of  the  bill  within  a  specified  time, 
as  30  days,  60  days,  or  90  days  from  the  date  of  shipment  or 
date  of  invoice.  In  most  cases  a  discount  of  from  2  %  to  6  % 
from  the  net  amount  of  the  bill  is  allowed  for  payment  in 
specified  time  before  the  bill  is  due.  Thus,  a  bill  that  is  due 
in  30  days,  when  so  specified  at  the  time  of  sale,  may  be  dis- 
counted 2%  in  10  days  from  date  of  sliipment.  Such  terms 
are  usually  written  "2%  10,  net  30"  or  "2/10,  n/30." 

197.  Discount  for  payment  according  to  terms  is  called 
cash  discoimt. 

198.  Various  kinds  of  merchandise  which  sell  only  during 
certain  seasons  are  often  made  up  and  shipped  several 
months  ahead,  and  bills  are  dated  ahead  accordingly.  For 
example,  holiday  goods  are  often  shipped  to  the  jobbers  in 
July  with  bills  dated  as  "Nov.  1st,  2%  10,  net  30."  Dress 
goods  for  spring  and  summer  wear  are  often  shipped  in 
January  and  dated  as  "April  1st,  6%  10,  net  60."     When  a- 


COMMERCIAL  DISCOUNT  125 

bill  is  paid  in  advance,  a  discount  of  ^  %  to  1  %  per  month  in 
excess  of  other  discounts,  called  anticipation,  is  usually  allowed. 

199.  In  commercial  discount. 

Face  of  bill  =  base. 

Per  cent  of  discount  =  rate. 

Discount  =  percentage. 

Net  amount  of  bill  =  difference. 

200.  Formulas: 

Face  of  bill  x  rate  =  discount,  or  BM  =  P. 

JP 

Discount  -h  rate  =  face  (3f  bill,  or  —=B, 

R 

P 

Discount  -T-  face  of  bill  =  rate,  or  —  =  i? . 

B 

Face  of  bill  —  discount  =  net  amount  of  bill. 

201.  Finding  the  net  price. 

The  tirst  price  of  a  certain  article  is  %  60.  If  this  price  is 
subject  to  a  discount  series  of  25%  and  20%,  what  is  the  net 
selling  price  ? 

25%  or  I  of  1 60  =  1 15,  first  discount. 

i  60  —  $  15  =  i  45,  price  after  the  first  discount. 
20  %  or  ^  off  1 45  =  I  9,  second  discount. 

1 45  —  I  9  =  1 36,  net  selling  price. 


Find  the  net  selling  price 

(by  inspection  when  possible) : 

List  Prick 

Rate  of  Discount 

1.                   $300 

20% 

2.                        50 

15% 

3.                        25 

10% 

4.                       75 

33^% 

5.                      125 

16f% 

6.                          3.75 

12|% 

7.                      750 

%\% 

8.                      100 

40% 

X 


X 


126  PERCENTAGE 

9.    A  buggy  listed  at  $  75  is  sold  less  33J  %  and  20  %. 
What  is  the  net  cost  of  the  purchase  ? 

10.  The  list  price  of  a  certain  book  is  1^.80,  subject  to  a 
discount  of  25%.  If  the  dealer  makes  10%,  what  is  his 
selling  price  ? 

11.  Find  the  net  amount  of  the  following : 

35  boxes  oranges  at  f  6.00 
12  doz.  cans  tomatoes  at  96^ 
20  bunches  bananas  at  $1.30 
Discounts  1^^%,  5%. 

12.  Which  is  the  better  offer,  and  how  much,  on  a  bill  of 
goods  amounting  to  $2000,  a  discount  series  of  30%,  20%, 
and  25%,  or  a  series  of  50%  and  12|  %? 

13.  The  net  price  of  an  article  is  i2.00.  If  discounts  of 
20  %  and  10  %  from  the  list  price  have  been  allowed,  what 
is  the  list  price?  [Net  price  h- (100%  —  discount)  =  list 
price.] 

14.  Columbus,  Ohio,  July  1,  1914. 

LOVEMAN,    JOSKPH,    &    LOEB 

BiRMiNGTON,    Ala.  t..  ^^^^.,.,*  .„;*u 

'  In  account  with 

«n/  -./^       .  r,/^  The  Morehouse  Manufacturing  Co. 

2%/ 10,  net  30. 

Dated  as  Nov.  1,  anticipation  1  %  a  month. 


^  gr.  Kum  Bak  Games  @  S48  per  gross 
2  doz.  Marathon  Racers  @  812  per  dozen 
I  doz.  3-way  Cars  @  S 18  per  dozen  .     . 
^  gr.  Hi-Lo  games  @  §24  per  gross    .     . 


What  was  the  amount  of  the  billJuly  10?   Nov.  1  ?   Dec.  1  ? 

15.  What  is  the  net  amount  of  a  bill  of  goods  amounting 
to  |?1250,  dated  Oct.  3,  terms  1|%/10,  1  %/30,  net  60, 
paid  on  Oct.  26  ?  What  would  be  the  discount  if  paid  on 
Oct.  8? 


COMMERCIAL  DISCOUNT  127 

16.  We  bought  of  Berry  Hros.  2000  -/g"  x  1"  roundhead 
stove  bolts  at  90^  per  hundred,  and  1000  -^^  "  x  11"  roundhead 
stove  bolts  at  il.15  per  hundred,  subject  to  discounts  'of 
85  %,  10  %,  and  10  %.     What  was  the  net  amount  of  the  bill  ? 

17.  An  article,  listed  at  $1.50,  is  sold  by  a  jobber  to  a 
merchant  at  a  net  wholesale  price  of  33^  %  off  list.  The 
jobber  gets  a  discount  of  25  %  off  the  net  wholesale  price, 
and  the  salesman  gets  a  commission  of  10  %  of  the  price  paid 
by  the  jobber.  If  the  labor  and  materials  cost  the  manu- 
facturer 25  j^,  and  his  overhead  charge  is  20%  of  the  net 
wholesale  price,  what  is  the  profit  to  the  manufacturer  ? 

18.  The  F.  P.  Hall  Co.  sold  the  following  bill  of  hardware: 
17  gross  #8  screws  at  SI  ^  per  gross,  less    87|-  %,   5%, 

10%,  5%,  71%. 

1§  doz.  locks  at  117.50  per  dozen,  less  50  %,  20  %,  10  %. 
I  doz.  locks  at  $12.60  per  dozen,  less  16|  %  and  7|  %. 
3  J  doz.  2 J  bolts  at  $1.25  per  dozen,  less  80  %  and  5  %. 
2^j  doz.  bolts  at  $3.60  per  dozen,  less  6b  %. 

What  was  the  net  amount  of  the  bill  if  discounted  2  % 
for  cash  ? 

202.    To  find  a  single  discount  equal  to  a  discount  series. 

In  extending  a  large  number  of  bills  from  which  must  be 
taken  the  same  series  of  discounts,  it  is  convenient  to  deter- 
mine a  single  discount  equal  to  the  quoted  discount  series. 

Find  a  single  rate  of  discount  equivalent  to  a  discount 
series  of  25  %  and  20  %. 

Solution  1 

1.00  (list  price  100  %) 
.25     (I  of  100%) 
.75 

.15     (iof75%) 
.60 
100  %  —  60  %  =  40  %  single  discount. 


128  PERCENTAGE 

Solution  2 

J+  6  —  2TF~  2Tr  ^^  ^'  ^  =  -t^  %         Wlien  the  discount  series  contains 
or  but  two  discounts,  from  the  sum  of 

25  %  +  20  %  —  5  %  =  40  %        the  discounts  subtract  their  product. 

Note.  —  If  the  discount  series  has  three  discounts,  find  a  single  per  cent 
equivalent  to  two  of  them,  and  then  a  single  per  cent  equivalent  to  the  first 
result  and  the  remaining  discount.  For  example,  if  the  above  series  had  been 
25%,  20%,  and  10%,  it  would  have  been  equal  to  a  series  of  40%  and  10%. 

Find  a  single  discount  equivalent  to  the  following  series 
of  discounts: 

1.  10  %  and  10  %  9.  20  %,  10  %,  and  10  % 

2.  25  %  and  25  %  /\  10.  40  %,  20  %,  and  10  % 

3.  20%  and  20%  >(  11.  16|%,  66|  %,  and  5  % 
^4.  40  %  and  20  %  ^^  12.  25  %,  10  %,  and  33^  % 
%5.    30%  and  20%  13.  25  %,  20  %,  and  16f  % 

6.  50  %  and  40  %  14.    20  %,  20  %,  and  12|  % 

7.  33J%  and  33J%  15.    12^  %,  6J  %,  and  5  % 

8.  33^  %  and  15  %  ^  16.    40  %,  20  %,  and  12J  % 

17.    A  firm  gives  its  customers  a  discount  series  of  25  %, 
20%,  and  10%.     What  single  discount  does  it  allow  ? 
\/18.    Goods  listed  at  $300  are  sold  subject  to  a  discount 
series  of  10%,  10%,  and  5%.     If  the  retail  merchant  sells  at 
a  profit  of  20  %  of  the  cost,  what  is  his  selling  price  ? 

MARKING  GOODS 

203.  Merchants  often  use  a  private  mark  to  indicate  the 
cost  and  selling  price  of  goods. 

Usually  some  word  or  phrase  is  selected,  containing  10 
different  letters,  to  be  used  as  a  key.  These  letters  repre- 
sent the  10  digits.  When  a  figure  is  repeated  some  letter  is 
used  to  represent  this. 

Note.     Some  merchants  have  different  keys  for  cost  and  selling  prices. 


MARKING  GOODS  129 

204.    Take  for  a  key,  "you  saw  them." 

123456T890         Repeater 
yousawthem  x 

Goods  which  cost  12.80  and  sell  for  $3.55,  would  be  marked, 


o.hm 


u.ax 


205.  To  show  20  %  profit. 

Goods  are  frequently  bought  by  the  dozen  and  sold  by 
the  piece,  or  bought  by  the  gross  and  sold  by  the  dozen. 
It  is  evident  that  if  10  articles  are  sold  for  the  cost  of  12, 
the  profit  is  2  articles  (^  of  10)  or  20%.  Thus,  if  ties  cost 
i5.00  per  dozen,  and  10  ties  are  sold  for  §5.00  (50  ^^  each), 
the  profit  will  be  20%. 

Hence  to  make  20%  profit,  mark  each  article  at  -^^  the 
cost  per  dozen  ;  or  mark  each  dozen  at  -^^  the  cost  per  gross. 
The  per  cent  of  profit  as  computed  is  based  on  the  cost. 

206.  To  show  more  than  20  %  profit. 

If  50^  each  for  the  above  ties  is  a  gain  of  20%,  it  is  a 
selling  price  of  120%.  To  show  a  profit  of  40%,  there  must 
be  a  selling  price  of  140%.  This  increase  of  20%  is  ^  of 
120  %.  Then  ^  of  50^  added  to  50^  gives  5Sy  (probably 
marked  at  60^). 

207.  To  show  less  than  20  %  profit. 

Subtract  the  aliquot  part. 

Mark  the  cost  and  selling  price  of  each  piece  by  the  above 
key: 

1.  Cost  i  12  per  dozen,  sold  at  a  gain  of  20  %. 

2.  Cost  $18.50  per  dozen,  sold  at  a  profit  of  30  %. 

3.  Boots  cost  $  26  per  dozen,  sold  at  a  gain  of  25  %. 

4.  Shoes  cost  $21.20  per  dozen,  sold  at  a  gain  of  25  %. 

5.  Shoes  cost  $17.50  per  dozen,  sold  at  a  gain  of  15  %. 

BUS.    AllITH. — 9 


130  PERCENTAGE 

6.  Pencils  cost  $5.00  per  gross,  sold  at  a  gain  of  10  % 
per  dozen. 

7.  Mark  the  selling  price  of  towels  bought  at  i2.90  per 
dozen  and  sold  at  a  gain  of  55  %. 

8.  Knives  bought  at  $3.60  per  dozen  are  sold  at  35  % 
profit.     Mark  the  cost  and  selling  price  of  each  knife. 

9.  Mark  shoes  costing  $  3.90  per  pair  so  as  to  gain  33  j  %. 

10.  By  selling  a  hat  at  $3.60,  I  gain  20%.  What  was 
the  cost  per  dozen  ? 

11.  A. merchant  bought  boots  at  $29.30  per  dozen.  He 
sold  them  at  a  profit  of  20  %  after  allowing  a  discount  of 
10  %  from  the  marked  price.     What  was  the  marked  price  ? 

12.  A  merchant  buys  silk  marked  at  $1.20  per  yard,  and 
gets  discounts  of  25  %  and  20  %.  Mark  the  goods  so  that  he 
will  gain  25  %. 

13.  Caps  are  listed  at  $  24  per  dozen.  The  discounts  al- 
lowed are  25,  20,  and  16|.     Mark  a  cap  so  as  to  gain  60  %. 

WHOLESALE   AND    RETAIL   PROFITS 

208.  In  most  wholesale  and  retail  businesses,  capital  is  re- 
quired :  (a)  for  the  first  cost  of  merchandise,  (5)  for  the 
cost  of  doing  business,  including  selling  expenses,  advertising, 
commissions  for  selling,  and  the  like. 

209.  Profit  is  the  difference  between  the  total  cost  and  the 
total  selling  price,  which  is  in  excess  of  the  cost. 

210.  Percent  of  profit  is  a  per  cent  of  all  money  invested. 
Since  it  is  not  possible  to  determine  all  moneys  invested 
until  the  goods  shall  have  been  sold,  and  since  the  cost  of 
doing  business,  including  commissions  for  selling,  must  be 
figured  on  the  selling  price,  it  is  advisable  to  figure  both  profits 
and  cost  of  doing  business  on  the  selling  price. 


WHOLESALE  AND   RETAIL  PROFITS 


131 


Note.  In  gain  and  loss  the  cost  was  used  as  the  base,  but  in  problems 
where  cost  of  doing  business  must  be  figured,  always  use  the  selling  price 
as  the  base. 

Illustration  : 

An  article  cost  $19.50,  cartage  50  j^.  If  the  cost  of  doing 
business  is  15%,  and  a  profit  of  10  %  is  to  be  made,  at  what 
price  must  the  article  be  sold  ? 

Selling  price  100  % 

Cost  of  doing  business  15  % 

Profit  desired  10  % 

Wholesale  cost  100  %  —  25  %  =  75  %  of  selling  price. 

119.50  +  .50  =  $20,  cost  in  money. 
120 -f-  .75  =  126.67,  selling  price. 

211.  The  following  Retail  Merchants'  Table  is  based  upon 
the  selling  price.     The  numbers  in  the  table  are  per  cents. 

Retail  Merchants'  Table 
table  for  finding  the  selling  price  of  an  article 


Cost 

OF 
DOING 

Busi- 
ness 

Net  Per  Cent  of  Profit  Desired 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

16 

20 

25 

30 

35 

40 

50 

15% 

84 

83 

82 

81 

80 

79 

78 

77 

76 

75 

74 

73 

72 

71 

70 

65 

60 

55 

50 

45 

35 

16% 

83 

82 

81 

80 

79 

78 

77 

76 

75 

74 

73 

72 

71 

70 

69 

64 

59 

54 

49 

44 

34 

17% 

82 

81 

80 

79 

78 

77 

76 

75 

74 

73 

72 

71 

70 

69 

68 

63 

58 

53 

48 

43 

33 

18% 

81 

80 

79 

78 

77 

76 

75 

74 

73 

72 

71 

70 

69 

68 

67 

62 

57 

52 

47 

42 

32 

li>% 

80 

79 

78 

77 

76 

75 

74 

73 

72 

71 

70 

69 

68 

67 

66 

61 

56 

51 

46 

41 

31 

20% 

79 

78 

77 

76 

75 

74 

73 

72 

71 

70 

69 

68 

67 

66 

65 

60 

55 

50 

45 

40 

30 

21% 

78 

77 

76 

75 

74 

73 

72 

71 

70 

69 

68 

67 

66 

65 

64 

59 

54 

49 

44 

39 

29 

22% 

77 

76 

75 

74 

73 

72 

71 

70 

69 

68 

67 

66 

65 

64 

63 

58 

53 

48 

43 

38 

28 

23% 

76 

75 

74 

73 

72 

71 

70 

69 

68 

67 

66 

65 

64 

63 

62 

57 

52 

47 

42 

37 

27 

24% 

75 

74 

73 

72 

71 

70 

69 

68 

67 

66 

65 

64 

63 

62  61 

56 

51 

46 

41 

36 

26 

25% 

74 

73 

72 

71 

70 

69 

68 

67 

66 

65 

64 

63 

62 

6l!60 

55 

50 

45 

40 

35 

25 

132  PERCENTAGE 

Rule.  Divide  the  cost  (invoice  price  with  freight  added)  by  the  figure 
in  the  column  of  "net  per  cent  profit  desired"  on  the  line  with  per 
cent  of  "  cost  of  doing  business." 

Example : 

If  a  wagon  costs $60.00 

Freight 1.20 

161.20 

A  net  profit  is  desired  of 5  per  cent 

It  costs  to  do  business 19  per  cent 

Take  the  number  in  column  5  on  a  line  with  19,  which 
is  76. 

80.526    (selling  price) 
i76)61  ^20.00 
60  8 
400 
380 
200 
152 
480 
456 

EXERCISES 

1.  An  automobile  cost  $800  at  the  factory,  freight 
i»  18.50;  at  what  price  must  it  be  sold  to  show  a  profit  of 
25  %  if  it  costs  20  %  to  conduct  the  business  ? 

2.  One  gross  of  brooms  cost  $26.50,  with  freight  charges 
of  $1.50.  If  it  costs  15%  to  do  business,  and  the  jobber 
wishes  to  secure  a  profit  of  15  %,  at  what  price  must  he  sell 
them  per  dozen  ? 

3.  A  car  of  coal  cost,  with  freight  added,  $108.  At 
what  price  must  it  be  sold  to  pay  expenses  of  21  %  and  a 
profit  of  7  %  ? 


COMMISSION 


133 


4.  A  piece  of  farm  machinery  cost  at  the  factory  S 214. 50. 
At  what  price  must  it  be  sold  to  show  a  profit  of  5  %  and 
cover  a  selling  expense  of  17  %  ? 

5.  A  stove  cost  118,  freight  82.  It  was  marked  at  a 
price  sufficient  to  cover  expenses  of  15  %  and  show  a  profit 
of  35  %.  If  it  was  sold  at  a  discount  of  10  %  from  marked 
price,  what  was  the  selling  price  ? 

6.  A  druggist  buys  toilet  articles  and  rubber  goods  to  the 
amount  of  f  100  each.  For  advertising  purposes  the  toilet 
articles  are  sold  at  cost.  If  the  selling  expense  of  both  is 
15  %,  at  what  per  cent  profit  must  the  rubber  goods  be  sold 
to  realize  10  %  on  the  entire  transaction  ? 

7.  Extend  and  foot  the  following  bill: 

Dayton,  Ohio,  Jan.  16,  1914. 
The  Kroger  Company, 

Columbus,  Ohio. 

In  account  with 
The   E.   C.    Harley   Company. 


2001b. 
1001b. 

50 

201b. 
200 
200 


No.  6  coffee  @  30^  .  .  . 
Dayton  roast  coffee  @  25^ 
boxes  laundry  soap  @  95^ 
currants  @  V2^  .  .  .  . 
doz.  canned  goods  @  $1.25 
doz.  canned  goods  @  95/' 


At  what  price  must  each  article  be  sold  to  realize  a  profit 
of  12%  if  the  expense  of  doing  business  is  18%? 


COMMISSION 

212.  Commission  or  brokerage  is  the  sum  charged  by  an 
agent  for  transacting  business  for  another. 

The  agent  is  called  the  broker,  commission  merchant,  or 
collector,  according  to  the  character  of    the  business  trans- 


134  PERCENTAGE 

acted.       The   one   for  whom  the   business  is  transacted   is 
called  the  principal. 

213.  A  guaranty  is  an  additional  charge  made  by  the 
agent  for  assuming  the  risk  on  credit  sales,  or  for  the  quan- 
tity and  quality  of  goods. 

214.  Merchandise  sent  by  a  principal  (shipper  or  con- 
signor) is  called  a  shipment. 

215.  Merchandise  received  by  an  agent  (consignee)  is 
called  a  consignment. 

216.  Gross  proceeds  is  the  total  amount  received  by  the 

agent  for  the  goods. 

217.  Net  proceeds  is  the  amount  remaining  after  all  ex- 
penses have  been  deducted. 

218.  The  prime  cost  is  the  actual  cost  of  the  merchandise. 

219.  The  gross  cost  is  the  total  cost,  including  expenses,  etc. 

220.  An  accoimt  sales  or  account  purchase  is  a  statement 
itemizing  the  entire  transaction. 

221.  Apply  the  principles  of  percentage. 
Gross  proceeds  or  prime  cost  =  base. 
Rate  of  commission  =  rate. 
Commission                               =  percentage. 
Gross  cost  or  gross  proceeds  =  amount. 
Net  proceeds                              =  difference. 

Formulas : 

Gross  proceeds  or  prime  cost  x  rate  of  commission  =  com- 
mission,  or  ^^^^_ 


COMMISSION 


135 


Commission  -f-  rate  =  gross  proceeds  or  prime  cost,  or 


R 


B. 


Commission  -=-  gross  proceeds  or  prime  cost  =  rate,  or 


B 


B. 


Prime  cost  4-  commission         =  gross  cost. 
Gross  proceeds  —  commission  =  net  proceeds. 


EXERCISES 

Supply  the  missing  parts  (by  inspection) 


Gross  Proceeds 

Rate  of 

COMiMlSSION 

Commission 

Net  Proceeds 

1. 

$4500 

n 





2. 

1800 

12i 

— 

— 

3. 

1200 

n 

— 

— 

4. 

1260 

3 

— 

— 

5. 

1600 

H 

— 

— 

6. 

1800 

16| 

— 

— 

7. 

7500 

1500 

— 

8. 

1400 

— 

400 

— 

9. 

1500 

— 

600 

— 

10. 

1800 

— 

400 

— 

Supply  the  missing  part : 

Gross  Proceeds 

Kate  of 
Commission 

Kate  of  Gifarantv 

Net  Proceeds 

11. 

$  4500 

2i 

2 



12. 

1800 

10 

— 

1530 

13. 

12000 

— 

2i 

9700 

14. 

1350 

5 

1 

— 

15. 

1200 

121 

— 

— 

136 

16. 


PERCENTAGE 
Account  Sales 


20000  lb.  of  coal 

.$4       per  ton 

KJOOO  lb.  of  coal 

$3,50  per  ton 

— 

40000  lb.  of  hay 

$  12     per  ton 

— 

60  T.  of  hay 

$10     per  ton 

— 

3000  lb.  of  wheat 

70^     perbu. 

— 

7000  lb.  of  oats 

60^      per  bu. 



1500  lb.  of  corn  (shelled) 
Charges 

80^     per  bu. 



.__ 

Freig^ht,  .$250;  storage,  $136 

drayage,  $60; 

insurance,  -^10. 

• 

— 

Commission,  6% 

Net  Proceeds 



— 



— 

17.  An  agent's  commissions  were  ^2500  in  one  month.  If 
he  transacted  business  on  a  5%  commission,  how  much  busi- 
ness did  he  handle  that  month? 

18.  An  agent  sold  40000  lb.  of  wheat.  After  deducting 
his  commission  of  2%,  he  sent  his  principal  -1490.  For  how 
much  per  bushel  was  the  wheat  sold  ? 

19.  A  manufacturer  remits  his  agent  f  3150  with  which  to 
buy  cotton.  How  much  does  the  agent  invest  if  his  com- 
mission is  5  %  ? 

[Amount  -f-  (1  -|-  rate)  =  investment.] 

20.  A  commission  mercliant  remits  #8000  to  invest  in 
wheat,  after  all  expenses  are  paid.  Charges  were  as  follows: 
guaranty,  2%;  drayage,  $10;  freight,  flOO;  commission, 
2^%.  Find  the  commission,  and  the  amount  actually  in- 
vested in  wheat. 

21.  A  salesman  for  a  wholesale  house  works  on  a  commis- 
sion of  5%.  On  sales  in  excess  of  $100000  per  year  he  gets 
an  added  1  %.  From  the  following  report  of  his  sales,  figure 
his  total  commissions,  and  his  net  income  above  expenses. 


MISCELLANEOUS  PROBLEMS 


137 


Month 

Sales 

Expenses 

Jan 

Feb 

$21673.85 
27421.96 
28316.40 
18629.90 
23718.06 
30163.46 

$521.60 
608.35 

March 

560.25 

July        

389.40 

August 

Sept 

465.75 
720.80 

Totals 

22.  A  salesman  is  guaranteed  a  salary  of  $2000  per  year, 
with  the  understanding  that  he  is  to  receive  not  less  than 
4%  of  his  total  sales.  What  is  his  income  in  cash  in  the 
following  years  ?  What  per  cent  of  his  sales  for  1910  did  he 
receive*  as  salary  ?  What  per  cent  of  his  sales  for  the  three 
years  is  his  income  for  that  time  ? 


Year 

Sales 

Income 

1910 

$41675.00 
52317.81 
64500.28 

1911 

1912 

Totals 

MISCELLANEOUS   PROBLEMS 
Group  1 

1.  Give  the  fractional  equivalent  for  the  following  per- 
centages :  5%,  6f%,  81%,  10%,  111%,  121%,  20%,  25%, 
331%,  50%,  621%,  75%. 

2.  If  ^=200  and  E=  .05,  find  P  in  the  equation  BR  =  P. 
.3.    If  ^=600  and  P=  200,  find  R  in  the  equation  BR  =  P. 


138 


PERCENTAGE 


4.  A  man  bought  a  drug  store  for  $  6000  ;  he  gave  a  mort- 
gage for  60  %  of  it.     What  was  the  amount  of  the  mortgage  ? 

5.  A  merchant  failing  in  business  was  able  to  pay  85% 
of  his  debts.     How  much  did  he  pay  A,  if  he  owed  him  f  4000  ? 

6.  A  man's  income  is  $1500  per  year.  His  expenses  are 
as  follows  :  rent,  $  300  ;  household,  $  500  ;  heat,  $  50;  light, 
$  20  ;  clothing,  $  200  ;  miscellaneous,  ilOO.  What  per  cent 
of  his  salary  does  he  save  ? 

7.  A  town  lot  is  valued  at  -f  2000,  caused  by  a  25  %  rise  in 
the  value  of  real  estate.  If  the  owner  valued  it  before  the 
rise  at  20  %  more  than  he  paid  for  it,  what  did  it  cost  him  ? 

8.  A  house  is  sold  for  $  10000,  at  a  loss  of  20  %  of  the  cost. 
Had  it  been  sold  for  $  15000,  what  would  have  been  the  per 
cent  of  gain  ? 

9.  A  man  bought  a  farm  for  $  6000.  Disregarding  inter- 
est, he  can  pay  for  the  property  in  12  years  by  saving  20  % 
of  his  income.     What  is  his  income  ? 

10.  A  merchant's  cost  of  doing  business  is  33J  %  of  his 
gross  sales  ;  his  profits  are  20%  of  his  gross  sales.  If  the 
gross  sales  for  the  year  1912  are  i  50000,  what  per  cent  of 
his  profits  is  his  cost  of  doing  business  ? 

Group  2 

In  applying  the  principles  of  percentage  to  the  solution  of  problems, 
as  in  Gain  and  Loss,  Commission,  etc.,  pick  out  B,  R,  and  P  before  at- 
tempting to  solve. 

1.    Supply  the  missing  parts  : 


Cost 

SEi.i.iNd  Prick 

Gain 

Loss 

Ratk 

$2500 

13000 

15000 

!|600 

1 6000 

20% 

1 15000 

6i% 



$2000 

20% 

MISCELLANEOUS  PROBLEMS 


139 


2.  An  article  is  sold  for  50  j^,  at  a  profit  of  15  j^.  What 
formula  can  be  applied  to  the  solution  of  this  problem  ?  What 
two  parts  are  given,  and  what  is  to  be  found? 

3.  Make  up  a  problem,  using  the  formula  —  =  P. 

4.  A  bought  50  hogs  for  i  325  ;  he  sold  them  so  as  to 
gain  16|  %  on  the  cost.    How  much  did  he  receive  for  each  hog  ? 

5.  A  trunk  is  manufactured  at  a  cost  of  §4.75.  It  is  sold 
at  a  profit  of  40  %  of  the  cost  by  an  agent  who  charged  a  com- 
mission of  10  %.     How  much  did  the  manufacturer  get  for  it  ? 

6.  A  clotliing  merchant  sold  a  suit  of  clothes  for  f  25.  If 
he  gained  33J  %  on  the  cost,  what  was  the  cost  of  the  suit  ? 

7.  An  automobile  which  cost,  when  new,  $1350,  was  sold 
a  year  later  for  1837.50.     What  was  the  per  cent  of  loss  ? 

8.  A  manufacturer  gained  115000  in  1911,  and  lost 
16700  in  1912.  If  the  capitalization  was  $75000,  what  was 
the  per  cent  of  gain  for  the  two  years  ? 

9.  A  commission  merchant  received  a  shipment  of  6000 
bu.  of  potatoes.  He  sold  16|%  of  them  at  $1.25  per  bushel ; 
331%  at  $1,121;  40%  at  $1.10  ;  the  remainder  at  cost.  If 
they  cost  him  $1  per  bushel,  how  much  did  he  gain? 

10.  A  bought  a  stock  of  merchandise  for  $  12000.  He  sold 
it  at  a  gain  of  20  %  of  the  cost,  but  was  unable  to  collect  20  %  of 
the  bill.    What  per  cent  of  the  cost  did  he  make  on  the  deal  ? 

Group  3 
1.    Find  the  missing  parts  : 


List  Price 

Net  Price 

Discount 

Eate  of  Discount 

1300 

$18 

$250 

$50 

50^ 

^% 

$75 

16|% 

87  J^ 

7% 

140  PERCENTAGE 

2.  A  dealer  can  buy  the  same  line  of  goods  from  either  of 
two  wholesale  houses.  The  first  offers  him  discounts  of 
20%  ,  15%,  and  5%;  the  second  offers  25%,  10%,  and  5%. 
Which  offer  is  the  better,  and  how  much  ? 

3.  A  gas  company  offers  a  discount  of  5^  per  thousand 
cubic  feet  off  the  contract  price  of  85^  per  thousand  cubic 
feet  on  bills  paid  before  the  10th  of  each  month.  What 
per  cent  of  each  bill  is  saved  by  taking  advantage  of 
the  offer? 

4.  Which  is  greater,  a  discount  series  of  15%,  20%,  and 
5%,  or  a  straight  discount  of  40  %  ? 

5.  A  merchant  bought  a  bill  of  goods  on  terms  2%/10, 
net  30.  He  paid  the  bill  5  da.  after  its  date,  thereby  saving 
117.     What  was  the  face  of  the  bill  ? 

6.  A  wholesaler  sold  ten  bills  of  goods  to  customers, 
allowing  on  each  discounts  of  25%,  10%,  and  5%.  What 
were  the  discounts,  if  the  bills  were  as  follows:  #135.68, 
#820,  $56.70,  1301, 1827.32,  #26.81,  #443.49,  #72.50,  #625, 
#281.33? 

7.  The  net  proceeds  of  a  bill  on  which  discounts  of  10  % 
and  5%  had  been  allowed  were  #256*50.  What  was  the  face 
of  the  bill  ? 

8.  An  article  listed  at  #1.20  cost  a  dealer  72^.  If  the 
first  discount  was  20  %,  what  was  the  second  discount  ? 

9.-  Goods  listed  at  #50  are  discounted  40%  and  33 J  % 
to  a  retailer.  What  discount  must  the  retailer  give  off 
the  list  price  in  addition  to  40%  in  order  to  gain  25%  of 
the  cost? 

10.  What  is  the  net  discount  of  the  following  bill,  if  paid 
on  April  1  ?  What  would  it  have  been,  if  paid  March  1, 
anticipation  being  1|  %  per  month? 


MISCELLANEOUS  PROBLEMS 


141 


Feb.  1,  1914. 


0.  J. 

yilLLER, 

Mt.  GiLEAD,  Ohio. 

In  account  with 

BURLEY   &   STEVENS,  Inc. 
2/30,  net  60 
Date  April  1 

18 
18 
16 
20 
12 

pr.  Boys'  grade  #8134  @  $2.15 
pr.  Boys'  grade  #8163  @  $2.40 
pr.  Boys'  grade  #  9143  @  11.85 
pr.  Boys'  grade  #8163  0  @  $2.25 
pr.  Boys'  grade  #8143a  @  |1.75 

Group  4 

1.  Using  the  key  in  §  204,  mark  shoes  costing  $2.40  a 
pair  so  as  to  gain  Q^^%. 

2.  The  following  price  tag  was  put  on  a  sweater  :   — '—^  . 

What  per  cent  of  the  cost  is  the  profit  on  the  sweater?     (Use 
key  in  §  204.) 

3.  Make  up  a  key  for  marking  goods  similar  to  the  one 
in  §  204.  Make  a  price  tag  showing  cost  per  piece  on  an 
article  costing  f  24  per  dozen,  and  a  selling  price  per  piece  to 
gain  30%.     (§206.) 

4.  A  suit  of  clothes  costing  $6.50  is  marked  to  sell  at 
'f  10,  but  is  sold  for  $9.87.  What  per  cent  of  the  cost  is 
sacrificed  by  selling  below  the  marked  price? 

5.  A  merchant  marked  an  article  costing  50/  to  sell  at 
75/,  thinking  he  was  making  a  net  profit  of  50%.  If  his 
cost  of  doing  business  is  20  %,  at  what  should  he  have  sold 
it  in  order  to  make  actually  50  %  profit  ? 

6.  Property  costing  $4800  is  sold  to  net  the  owner  20% 
profit  after  paying  a  commission  for  selling  of  5%.  For 
what  price  does  it  sell  ?     (§  211.) 


142  PERCENTAGE 

7.  The  capital  employed  in  a  state's  industries  is 
1 1,300,732,732,  and  the  expense  of  operating  is  1 1,282,845,514. 
What  per  cent  of  the  capital  is  the  operating  expense  ? 

8.  A  farmer  can  buy  machinery  at  the  manufactory  for 
$138,  less  3%  for  cash,  and  it  will  cost  him  fl2  freight 
charges  to  ship  it  to  his  home.  Is  it  better  to  buy  at 
this  price,  or  at  $150  delivered  at  his  home,  less  3% 
for  cash? 

9.  An  agent  purchased  250  bales  of  cotton  at  $12.02  per 
bale.     What  is  his  commission  at  1|  %  ? 

10.  A  real  estate  firm  charges,  as  commission,  5  %  of  the 
first  $2500  involved  in  any  transaction,  and  2%  of  any 
amount  over  the  first  $2500.  What  will  it  receive  for  sell- 
ing property  for  $4000?  for  $5300  ?  for  $1625?  for  $108000? 
for  $17783.60? 

Group  5 

1.  A  man  bought  1000  bu.  of  wheat  at  $1.01i  per  bushel, 
and  5000  bu.  of  corn  at  44|  ^  per  bushel.  He  sold  the 
wheat  for  $1.02|  per  bushel,  and  the  corn  at  43 J  ^  per 
bushel.     How  much  was  his  gain  or  loss  ? 

2.  An  apartment  building  cost  the  owner  $28000,  and 
he  estimates  his  yearly  expenses  as  follows:  taxes,  $310; 
insurance,  $60;  water,  $70;  janitor,  $300;  fuel,  $460; 
repairs,  $120.  What  yearly  rental  must  he  get  from  each 
of  12  apartments  to  net  him  6%  on  his  investment? 

3.  A  creditor  agrees  to  settle  a  debt  at  90  ^  on  the  dol- 
lar. He  receives  $5327.38,  after  paying  a  commission  of 
2  %  for  collecting.     What  was  the  amount  of  the  debt  ? 

4.  A  commission  merchant  receives  $42.18  in  payment 
of  a  commission  of  2%  and  expenses  of  $3.10.  What  was 
the  amount  of  the  sale  ? 


MISCELLANEOUS  PROBLEMS 


143 


5.  A  life  innurance  agent  receives  30  %  of  all  premiums 
on  new  business.  If  the  average  premium  paid  on  his  new 
business  is  #31.50,  how  many  premiums  will  he  have  to 
secure  to  earn  an  income  of  f  1956.15? 

6.  For  what  must  property  be  sold  to  net  the  owner 
$8730  after  paying  a  commission  of  3%  for  selling? 

7.  Property  selling  for  18250  pays  the  agent  negotiating 
the  sale  3|^%  commission.  If  it  nets  the  owner  12^  %  profit 
on  the  cost,  how  much  did  it  cost  ? 

8.  Property  costing  13100  sells  for  $3750.  If  the  sell- 
ing agent  receives  a  3  %  commission,  what  per  cent  of  the 
gross  profit  goes  to  the  selling  agent  ? 

9.  A  retail  merchant  takes  in  $800  a  month  at  an  ex- 
pense of  $200  a  month.  At  what  must  he  sell  an  article 
costing  him  25  j^  in  order  to  net  15  %  ? 

10.  What  is  the  total  amount  of  commissions  received  by 
a  professional  shopper  in  a  large  city,  who  purchases  tlie 
following  goods : 


Bought  for 

Article  and  Prick 

Amount 

Rate 

Com. 

Mrs.  A 

12  yd.  silk  @  $1.25      .     . 
8  yd.  lace  @  87  ^  .     .     . 

5% 

Mrs.  B 

1  brass  bed,  $32.50     .     . 
1  dresser,  $21.75   .     .     . 

1% 
6% 

Mrs.  C 

6  pr.  gloves  @  $1.35  .     . 
6  pr.  hose  @  85  ^  .     .     . 
2doz.  hdkfs.  @  35j^  each 

Mrs.  D 

1  umbrella  @  $5.60    .     . 

«% 

INTEREST 

222.  Interest  is  an  allowance  made  for  the  use  of  money. 

223.  Three  factors  enter  into  interest  calculations,  viz., 
principal,  rate  per  cent,  and  time. 

224.  Certain  per  cents  are  allowed  by  law.  The  legal 
rate  ranges  from  5%  to  8%  in  the  different  states. 

Any  charge  above  the  rate  allowed  by  law  is  called  usury, 
and  is  prohibited  under  various  penalties  in  different  states. 

Note.  Debts  of  all  kinds  are  subject  to  interest  from  the  time  they 
become  due,  but  not  before,  unless  specified. 

225.  Interest  is  commonly  computed  on  360  da.  to  the 
year,  30  da.  to  the  month,  and  12  mo.  to  the  year.  This  is 
called  common  interest.  Time  less  than  one  year  is  found 
by  counting  the  actual  number  of  days.  Long  periods  of 
time  are  found  by  compound  subtractions.  Hate  is  by  the 
year,  unless  otherwise  specified. 

226.  Interest  formulas  : 

Principal  x  rate  x.  tiipe  (in  years)  =  interest,  or  PIiT=  I. 

Interest  -^  (rate  x,  tin^e)  =  principal,  or  ■^-s^=  P- 
Interest  -f-  (principal  x  time)  =  rate,  or  ^^=  R- 
Interest  -^  (principal  x  rate  )  =  time,  or  — —  =  T, 

JT  til 

Principal  +  interest  =  amount,  or  P  -f-  PUT  —  A. 

227.  (a)  Find  the  interest  on  $200  for  4  mo.  at  6.%. 
Find  the  amount. 

PRT=  J,  where  P  =  $  200,  R  =  .06,  and  T  =  \. 

144 


INTEREST 


145 


Substituting  these  values  in  the  equation,  we  have 
1200  X  .06  X  ^  =  14,  interest. 
.$  200  +  I  4  =  $  204,  amount. 

(b)    What  principal  will  amount  to  f  240  in  4  yr.  at  5%? 

F  +  PET=A. 

A 


1+RT 

240 


Factoring,     P(\  +  RT)  =  A,  P= 

Substituting  the  values  P  = 

Solving,  240  -i- 1 . 2  =  $  200,  principal. 

228.    Supply  the  missing  parts  : 


Principal 

Kate 

Time 

Interest 

Amount 

1. 

$75 

6% 

3yr. 

— 

— 

2. 

$150 

4% 

Hyr. 

— 

— 

3. 

$125 

— 

lyr. 

$625 

— 

4. 

$300 

7% 

— 

$84 

— 

5. 

— 

5% 

Syr. 

$75 

— 

6. 

— 

H% 

4  yr. 

— 

$1180 

7. 

$  1200 

— 

2  yr.  6  mo. 

$105 

— 

8. 

$1000 

5% 

1  yr.  4  mo. 

— 

— 

229.   Cancellation  method. 

Find  the  interest  on  $  350.50  for  1  yr.  2  mo.  11  da.  at  6  %. 

1    yr.    2    mo.    11    da.  =  431 


1350.50 

""lOO 

481 
'^360 

=  int. 

$350.50 

x481 

X0_ 

$151065.50 

100 

xm 

60 

6000 

$151.0655- 

-^6  = 

$25.18  int. 

BUS.    ARITH.  — 

10 

da.  ;  this  is  reduced  to  years 
by  dividing  by  360.  In  ap- 
plying the  formula  PRT  =  I, 
cancel  6  into  360.  In  dividing 
by  6000,  move  the  decimal 
point  3  places  to  the  left  and 
divide  by  6.  Hence,  to  Jind 
the  interest  at  6%,  multiply  the 
principal  hy  the  number  of  days, 
move  the  decimal  point  3  places 
to  the  left,  and  divide  hy  6. 


146  INTEREST 

Find  the  interest  on  f  7563  at  6  %  for  197  da. 

\  im 

^  \  2521  The  form  here  used  is  the  most  convenient 

2  \   197  ^^^  canceling  and  performing  the  other  neces- 

yiTrTjq  sary  operations.     Cancel  3  into  7563  and  into 

6;  multiply  2521   by  197  without  recopying; 

divide  the  result  by  2,  and  point  off  3  places 


22689 


2521  in  the  result. 


) 496637 
248.3185     $248.32,    int. 

230.  To  find  the  interest  at  any  other  rate  than  6  %. 
Add  or  subtract  the  necessary  aliquot  part  to  the  interest 
at  6  %. 

If  the  rate  in  the  above  problem  had  been  5  %,  find  the 
interest. 

6)$  248.3185 

41.3864  =  int.  at  1  %  (1  %  is  J  of  6  %). 
i  206.93      =  int.  at  5  %  (Subtraction). 

Note.  In  all  problems  involving  dollars  and  cents,  carry  the  decimal 
places  to  the  final  result,  then  if  the  figure  in  mills  is  5  or  more,  add  1 
to  the  cents  in  the  result;  if  less  than  5,  drop  it.  Many  mistakes  in 
bookkeeping  and  office  work  can  be  avoided  by  observing  this  rule. 

Find  the  interest : 


Principal 

Ratb  % 

Time 

1. 

i     300 

6 

3  yr.  3  mo. 

5  da. 

2. 

450 

4 

7  mo. 

6  da. 

3. 

248.25 

5 

2  yr.  9  mo. 

4. 

796.50 

6 

1  yr.  3  mo. 

15  da. 

5. 

503.40 

3 

90  da. 

6. 

872 

8 

93  da. 

7. 

897.50 

6 

143  da. 

8. 

15000 

5 

3  yr.  5  mo. 

17  da. 

9. 

5000 

6 

60  da. 

10. 

9000 

4 

35  da. 

INTEREST  147 

231.  eo-day  method. 

60  days  is  ^  of  one  year  (860  da.),  J  of  6%  =  1  %. 
The  interest  for  60  da.  at,  6%  is  therefore  1%  of  the 
principal. 

The  interest  on  |50  at  6%  for  60  da.  would  be  f0.50; 
therefore,  to  find  the  interest  for  60  da.  at  6  %,  point  off  two 
places  to  the  left  of  the  decimal  point. 

232.  If  the  per  cent  is  other  than  6  %,  find  the  proper 
aliquot  part  of  the  interest  at  6  %. 

233.  Time.  If  the  time  is  other  than  60  da.,  add  or  sub- 
tract the  proper  aliquot  part  of  60  da. 

Find  the  interest  on  1750  at  5%  for  80  da. 

$   7.50  =  interest  for  60  da.  at  6  % 

2.50  =  interest  for  20  da.  at  6% 

6)tl0.00  =  mterest  for  80  da.  at  6% 

1.67  =  interest  for  80  da.  at  1  % 


f  8.33  =  interest  for  80  da.  at  5% 
Find  the  interest : 


1. 

Pkinoipal 

1     98 

Kate  % 

6 

Time 

60  da, 

2. 

150 

7 

60  da. 

3. 

240 

8 

90  da. 

4. 

1450 

^  a 

less  than 

6%) 

72  da. 

5. 

2380 

61 

33  da. 

6. 

868.40 

4 

120  da. 

7. 

1000 

H 

75  da. 

8. 

850.75 

6 

54  da. 

9. 

790 

4 

1 

mo.     20  da. 

10. 

575.34 

5 

2 

mo.     18  da. 

148 


INTEREST 


234.  Six  per  cent  method. 

The  interest  on  11  at  6%  for  1  yr.  is  6^. 

Then  it  will  be  1^  for  60  da.,  and  1  mill  for  6  da.     Why  ? 

Find  the  interest  on  12340.20  at  7  %  for  2  yr.  2  mo.  15  da. 
'f0.12     =mt.onilfor    2yr.at6%. 

.01     =int.onilfor    2mo.at6%  (2mo.  =  J^  of  2yr.). 
.0025==int  on  $  1  for  15da.  at6  %  ri5  (la.  =  j  of  2  mo.). 
$0,132  5  =  int.  on^lfor    2  yr.  2  mo.  15  da.  at  6%. 
2340.20 
265  00 
5  300 
39  75 
265  0 


6)310.076500  =  int.  on  $2340.20  at  6  %. 
51.6794      =  int.  on  12340.20  at  1%. 
1361.7559     =  $361.76,  int.  at  7  %. 


Find  the  interest  and  amount 


1. 

Principal 

$758.12 

Ratk  % 

6 

2. 

896.50 

6 

3. 

3500. 

4 

4. 

450.75 

5 

5. 

185.54 

6 

6. 

1000. 

8 

7. 

3428. 

6 

8. 

26250. 

3 

9. 

7368.58 

2 

10. 

596.33 

H 

TlMB 

1  yr.  2  mo.  12  da. 

2  yr.  4  mo.  15  da. 

3  yr.  4  mo.  18  da. 

6  mo.  24  da. 
1  yr.  5  mo.    6  da. 

4  yr.  3  mo.  19  da. 
from  Apr.  3  to  July  25. 
from  5/20/09  to  11/24/12. 
from  2/10/04  to  5/18/06. 
from  1/10/11  to  12/21/12. 


INTEREST 


149 


235.  Simple  interest 
table. 


The  accompanying 
table  shows  the  inter- 
est on  11000  from  1 
da.  to  1  mo.,  and  1 
mo.  to  6  mo.  at  3  %  to 
7%.  For  instance, 
11000  will  earn,  in  20 
da.,  12.22  at  4%,  and 
12.77  at  5%.  In  2 
mo.,  11  da.,  it  will 
earn,  at  7  %,  111.66 + 
12.13,  or  ii  13.79. 

236.  To  find  what 
$100,  $750,  or  any 
other  aliquot  part  of 
$  1000  will  earn,  deter- 
mine the  amount  for 
$1000  from  the  table, 
and  take  the  necessary 
aliquot  part  of  it. 
Thus:  What  will $275 
earn  in  5  mo.  and  21 
da.  at  6  %  ? 


$1000  earns      $28.50. 
$  250  earns  J  of  this, 

or     $7,125. 


DATS 

3% 

4% 

5% 

6% 

1% 

1 

1.08 

$.11 

$.13 

$.16 

$.19 

2 

.16 

.22 

.27 

.33 

.38 

8 

.25 

.33 

.41 

.50 

.58 

4 

.33 

.44 

.55 

.66 

.11 

5 

.41 

.55 

.69 

.83 

.97 

6 

.50 

.66 

.83 

1.00 

1.16 

7 

.58 

.77 

.97 

1.16 

1.36 

8 

.66 

.88 

1.11 

1.33 

1.55 

9 

.75 

1.00 

1.25 

1.50 

1.75 

10 

.83 

1.11 

1.38 

1.66 

1.94 

11 

.91 

1.22 

1.52 

1.83 

2.18 

12 

1.00 

1..33 

1.66 

2.00 

2.33 

13 

1.08 

1.44 

1.80 

2.16 

2.52 

14 

1.16 

1.55 

1.94 

2.33 

2.72 

15 

1.25 

1.66 

2.08 

2.50 

2.91 

16 

1.33 

1.77 

2.22 

2.66 

3.11 

17 

1.41 

1.88 

2.36 

2.83 

3.30 

18 

1.50 

2.00 

2.50 

8.00 

3.50 

19 

1.58 

2.11 

2.63 

3.16 

3.69 

20 

1.66 

2.22 

2.77 

3.33 

3.88 

21 

1.75 

2.83 

2.91 

3.50 

4.08 

22 

1.83 

2.44 

3.05 

3.66 

4.27 

23 

1.91 

2.55 

3.19 

3.83 

4.47 

24 

2.00 

2.66 

3.33 

4.00 

4.66 

25 

2.08 

2.77 

3.47 

4.16 

4.86 

26 

2.16 

2.88 

3.61 

4.33 

5.05 

.   27 

2.25 

8.00 

3.75 

4.50 

5.25 

28 

2.83 

3.11 

3.88 

4.66 

5.44 

29 

2.41 

3.22 

4.02 

4.83 

5.63 

Months 

1 

2.50 

3.33 

4.16 

5.00 

5.83 

2 

5.00 

6.66 

8.33 

10.00 

11.66 

3 

7.50 

10.00 

12.50 

15.00 

17.50 

4 

10.00 

13.33 

16.66 

20.00 

23.33 

5 

12.50 

16.66 

20.83 

25.00 

29.16 

6 

15.00 

20.00 

25.00 

30.00 

35.00 

25  earns  ^^  of  $7,125,  or  $, 


.7125. 
$  275  earns  $7.125 +  $.7125,  or  $7.84. 


150  INTEREST 

EXERCISES 

Find  the  interest  on  : 

1.  1300  for  18  da.  at  5%. 

2.  $125  for  1  mo.  10  da.  at  4  %. 

3.  $260  for  3  mo.  5  da.  at  7  %• 

4.  $55  for  2  mo.  at  6%. 

5.  $100  for  1  mo.  at  2%.     (2%isJof4%.) 

6.  11000  for  15  da.  at  J  %. 

7.  ilOOO  for  23  da.  at  3 J  %. 

8.  $1500  for  4  mo.  19  da.  at  41  %. 

9.  $825  for  6  mo.  21  da.  at  51%. 

10.  $33.33  for  5  mo.  17  da.  at  6^  %. 

11.  How  much  does  a  man  lose  if  he  allows  $  2000  to  lie 
idle  for  30  da.,  when  money  is  worth  5  %  ? 

12.  What  is  the  earning  power  of  $100  at  6%  for  8  mo. 
15  da.? 

13.  If  $1800  lies  idle  for  1  mo.  20  da.,  what  is  the  loss 
at  41%? 

14.  A  man  refuses  to  lend  $  50  at  7  %  for  4  mo.  What 
amount  of  interest  does  he  sacrifice  in  refusing  ? 

15.  A  depositor  allows  $3725  to  remain  in  the  bank  from 
May  4  to  Nov.  4.  If  he  had  transferred  the  money  to  a 
savings  account  at  3^  %,  how  much  would  he  have  gained  in 
interest  ? 

16.  Find  the  interest  on  $3000  at  6%  from  Nov.  15, 1912, 
to  May  10,  1913. 

17.  In  Ohio,  a  Loan  Co.  may  deduct  10  %  of  the  loan  and 
charge  8  %  interest  on  the  total  amount.  How  much  interest 
is  received  on  a  $100  loan  for  4  months  ? 


EXACT   INTEREST  151 

SPECIAL    INTEREST    METHODS 
237.    (a)  Find  the  interest  on  $854.30  for  93  da.  at  8%. 

Principal  x  time  (in  years)  x  rate  =  inter- 

\  ^854.30  est.     As  the  time  is  expressed  in  days,  divide 

^^\  ^^  31  this  product  by  360  (by  36  and  move  the  deci- 

^-\a     \  g     2  '"^1  point  1  place  to  the  left).     Hence,  divide 

C-H9  V  ^1  ^   ^^®   product   of  the   principal,   the   number  of 

^  ^   days,  and  the  rate,  by  360. 

1  <0860  Notice  that  the  rate  is  per  cent  in  pointing 

51  2580  off  decimal  places  in  the  result.     In  the  illus- 

3)52.96(360  tration,  point  off  5  places,  2  for  the  cents  in  the 

1kl7  655       int  principal,  2  for  the  hundredths  in  the  rate,  and 

1  for  canceling  the  0  in  360. 

(ft)  Find  the  interest  on  $658  at  5%  for  6  mo. 

The  interest  at  5  %  for  6  mo.  is  the  same  as  the 
4)$  65.80  interest  at  10%  for  3  mo.     Hence,  to  find  the  interest 

$16.45    int.       at  5%,  point  off  1  place  to  the  left,  and  find  the 
aliquot  part  ^  the  time  is  of  one  yr. 


((?)  Find  the  interest  on  $  300  at  8  %  for  6  mo. 
$300 
.04 


Double  the  time  and  take   |  the  rate,  or  double  the 


rate  and  take  h  the  time,  as  in  (a). 
$  12,     int. 

(d)  Find  the  interest  on  $212.56  for  2  mo.  18  da.,  at  6%. 

$  ^12. 56  g-j^pg  ^j^g  interest  on  ^  1  at  6  %  is  I  ^  per 

'01^  month,  or  |^  of  a  mill  per  day,  one  half  the 

63768  number  of  months,  and  one  sixth  the  num- 

2  12.56  ^^^  ^^  days  may  be  written  as  the  cents 

$2.76328  =  $2.76,  int.      ^°^  ™^^^'  ^^  *^'^  multiplier. 

EXACT   INTEREST 

238.  Exact  interest  is  computed  on  a  basis  of  365  days  to 
the  year.  Exact  interest  is  rarely  used  except  in  govern- 
ment calculations.     365  days  is  5  days  more  than  common 


152 


INTEREST 


interest.     Five  days  is  y^^  of  365,  therefore,  to  find  the  exact 
interest,  find  the  interest  by  any  of  the  above  methods  and 


subtract  y^^  of  it. 

Find  the  exact  interest : 

Principal 

Rati 

TiMR 

1.    i700 

6% 

80  da. 

2.    $800 

4% 

75  da. 

3.   $975 

2% 

15  da. 

4.    i  812.25 

6% 

144  da. 

5.    $7368.90 

4% 

13  da. 

6.  A  savings  bank  pays  4%  interest  on  its  deposits.  It 
lends  money  at  6%.  If  its  deposits  amount  to  #237458.50 
and  its  loans  amount  to  $  192546,  what  is  its  gain  per  year  ? 
(Exact  interest  paid  yearly.) 

7.  A  manufacturer  ordered  a  bill  of  goods  amounting  to 
f  3548.60.  The  terms  were  3  mo.,  5  %  off  for  cash.  He 
paid  cash.     Find  his  gain,  using  6  %  simple  interest. 

8.  A  corporation  is  allowed  1 J  %  annual  rate  on  its  aver- 
age daily  balance  in  a  bank,  the  same  to  be  credited  every 
month.     Fill  in  the  allowance  by  simple  interest. 


Month 

AvEBAOB  Daily  Balance 

Allowance 

Jan 

Feb 

March 

April 

May 

June 

July 

Aug 

Sept 

Oct 

Nov 

Dec 

$73210.90 
61740.89 

125608.34 
53217.98 
90020.07 
70663.24 
81210.37 
53721.62 
74889.75 
96271.49 

163618.52 

181241.13 



COMPOUND  INTEREST  153 

COMPOUND    INTEREST 

239.  Compound  interest  is  interest  upon  principal  and 
added  interest.  Interest  is  added  at  stated  periods,  3 
months  (quarterly),  6  months  (semiannually),  or  12  months 
annually). 

240.  Many  transactions  are  computed  by  compound  inter- 
est. Savings  banks  and  insurance  companies  use  this 
method,  and  returns  on  bond  investments  are  reckoned  by 
compound  interest. 

241.  To  find  compound  interest  and  amount. 

Find  the  compound  interest  on  I  2000  for  3  yr.,  at  6  %, 
interest  compounded  yearly. 

Solution  1 

$  120,  interest  for  the  first  year. 
I  2000  +  I  120  =  12120,  principal  for  second  year. 
$2120  X  6%  =  $127.20,  interest  for  second  year. 
$2120  +  i  127.20  =  I  2247.20,  principal  for  third  year. 
•f  2247.20  X  6%  =  $134.83,  interest  for  third  year. 
$120  +  $127.20  4-  $134.83  =  $  382.03,  compound  interest. 

Solution  2 

$2000  X  6%  =  $  120,  interest  for  first  year. 
$  120  X  6  %  =$7.20,  interest  on  interest. 
$  120  +  $  7.20  =  $  127.20,  interest  for  second  year. 
$127.20  +  $120  =  $247.20,    compound    interest   for  two 
years. 

$247.20  X  6  %  =  $14.83,  interest  on  interest. 

$120  4-  $14.83  =  $134.83,  interest  for  third  year. 

$120  4-  $127.20 +  $134.83  =  $382.03,  compound  interest. 

Note.     Solution  1  is  generally  used. 


154 


INTEREST 


242.    Compound  interest  is  generally  computed  by  using 
the  compound  interest  table. 

Table  showing  Amount  of  $  1  at  Compound  Interest  for  Any  Number 
OF  Years  not  exceeding  Ten 


Yr. 

2% 

8% 

8i% 

4% 

c% 

1 

1.0200  0000 

1.0300  0000 

1.0350  0000 

1.0400  0000 

1.0600  000 

2 

1.0404  0000 

1.0609  0000 

1.0712  2500 

1.0816  0000 

1.1236  000 

3 

1. 0012  0800 

1.0927  2700 

1.1087  1787 

1.1248  6400 

1.1910  160 

4 

1.0824  3210 

1.1255  0881 

1.1475  2300 

1.1698  5856 

1.2624  770 

5 

1.1040  8080 

1.1592  7407 

1.1876  8631 

1.2166  52J)0 

1.3382  256 

6 

1.12016242 

1.1940  5230 

1.2292  5533 

1.26.53  1902 

1.4185  191 

7 

1.1480  8567 

1.2298  7387 

1.2722  7926 

1.3159  3178 

1.5036  303 

8 

1.1716  5038 

1.2667  7008 

1.3168  0904 

1.3685  6905 

1.6938  481 

9 

1.1950  9257 

1.3047  7318 

1.3628  9735 

1.4233  1181 

1.6894  790 

10 

1.2189  9442 

1.3439  1638 

1.4105  9876 

1.4802  4428 

1.7908  477 

Note.  This  is  only  a  small  sectiou  of  a  compound  interest  table. 
Tables  giving  all  per  cents  for  a  long  period  of  time  can  be  secured  at 
any  savings  bank. 

243.  To  find  compound  interest  by  the  table  : 

1.  Payable  annually,  multiply  the  principal  by  the  amount 
(shown  in  the  table  under  the  proper  rate  and  time)  less  f  1. 

2.  Payable  semiannually,  take  J  the  rate  and  twice  the 
time,  less  f  1. 

3.  Payable  quarterly,  take  J  the  rate  and  four  times  the 
time,  less  $  1. 

Note.  ^1  is  subtracted  to  find  the  compound  interest;  the  table  gives 
the  compound  amount. 

244.  If  the  time  should  be  any  time  not  shown  in  the 
table,  multiply  the  amounts  for  the  proper  aliquot  parts  of 
the  time  ;  e.g.^  to  compute  the  compound  interest  for  20 
yr.  at  6  %,  multiply  1.7908477  by  itself,  giving  3.2071355. 


SINKING  FUNDS 


155 


Find  the  compound  interest  on  JB^tOO  for  5  yr.  at  3J  %. 

See  compound  interest  table, 
§  242.  The  amount  in  the  3^% 
cohimn  opposite  the  5th  year  is 
$1.18768631.  Since  this  is  the 
amount,  the  compound  interest  on 
$  1  is  1.18768631.  Then  the  com- 
pound interest  on  $400  will  be  400 
times  1 .18768631,  or  $75.07. 


400  X  $.18768631  =  $75.07 


Find  the  compound  interest  (by  table) 


Pbincipal 

Rate 

Time 

1. 

1  600 

3% 

8  yr. 

2. 

$1500 

6% 

4  yr. 

3. 

$  500 

4% 

3  yr.  (semiannually) 

4. 

11240 

8|-% 

2  yr. 

5. 

$  350 

4% 

3  yr.  (quarterly) 

6. 

$  590 

2% 

8yr. 

7. 

$  800 

6% 

5  yr.  (quarterly) 

8. 

11000 

81% 

9yr. 

9. 

$2370 

8% 

4yr. 

10. 

$5760 

6% 

6  yr.  (semiannually) 

11. 

$8320 

4% 

2  yr. 

12. 

$5980 

2% 

7yr. 

SINKING    FUNDS 

245.  A  sinking  fund  is  a  sum  set  aside  each  year,  at  com- 
pound interest,  sufficient  to  meet  a  certain  obligation  at  its 
maturity.  Cities  often  make  public  improvements  by  bor- 
rowing money  and  issuing  bonds  therefor.  Tiie  bonds  are 
payable  in  5,  10,  15,  or  more  years,  as  the  case  may  be. 
To  meet  these  bonds  at  maturity  a  sinking  fund  is  estab- 
lished.    A  series  of  equal  payments  is  called  an  annuity. 


156 


INTEREST 


246.    Table  showing  annuity  of  $  1  at  the  end  of  each  year 
from  1  to  10  yr. : 


Period 

8% 

4% 

5% 

6% 

1 

1. 

1. 

1. 

1. 

2 

2.03 

2.04 

2.05 

2.06 

3 

3.0909 

3.1216 

3.1625 

3. 1886 

4 

4.183627 

4.246464 

4.310125 

4.374616 

5 

6.309136 

6.416323 

5.526a31 

6.637093 

6 

6.468410 

6.632976 

6.801913 

6.976319 

7 

7.662462 

7.898294 

8.142008 

8.393838 

8 

8.892336 

9.214226 

9.M9109 

9.897468 

9 

10.169106 

10.582796 

11.026564 

11.491816 

10 

11.463879 

12.006107 

12.677893 

13.180796 

247.   To  find  an  annuity: 

1.  A  certain  city  makes  improvements  at  an  expense  of 
#300,000  and  sells  municipal  bonds  maturing  in  10  yr. 
To  pay  for  them,  at  3  %  interest,  what  sum  must  be  set  aside 
each  year  to  meet  the  bonds  at  maturity  ? 

An  annuity  of  $  1  for  10  yr.  at  3  %  is  $  11.463879.  Then  it  will  require 
as  many  dollars  to  amount  to  ^300,000  as  ^11.463879  is  contained  times 
in  $300,000,  or  $20169.16   Ans. 

2.  City  bonds  to  the  amount  of  #500,000,  maturing  in  10 
yr.,  were  issued.  A  sinking  fund  earning  5%  was  provided. 
What  should  be  the  annual  investment  in  the  sinking  fund  ? 

3.  For  the  erection  of  a  city  hall  §100,000  municipal  bonds, 
payable  in  8  yr.,  are  issued.  What  amount  must  be  laid 
aside  each  year  at  4%  compound  interest  to  redeem  the 
bonds^  at  maturity  ? 

4.  A  steel  company  sells  8500,000  worth  of  10-yr.  bonds, 
and  #100,000  worth  of  20-yr.  bonds.  The  sinking  fund 
earns  4%.  What  amount  must  be  provided  each  year  to 
retire  both  issues  at  maturity? 


BANKS   AND   BANKING 

248.  Practically  all  business  is  done,  directly  or  indirectly, 
through  banks ;  they  are  the  money  and  credit  centers  of 
the  community.     Their  most  important  functions  are : 

(1)  To  receive  funds  for  deposit. 

(2)  To  make  loans. 

(3)  To  transfer  funds.     (See  Exchange,  p.  201.) 

By  "  funds  "  is  meant  money,  checks,  or  any  other  form  of 
credit.  The  depositor  really  buys  bank  credit  which  he  can 
order  transferred  as  he  wishes. 

The  credit  department,  which  handles  the  loans,  is  one  of 
the  most  important  departments  in  a  bank.  In  this  depart- 
ment a  complete  record  is  kept  of  the  applicant's  solvency, 
viz. : 

(1)  An  application  blank,  filled  in  by  the  applicant,  stat- 
ing his  financial  condition. 

(2)  The  depositor's  average  balance  in  the  bank,  which 
helps  to  determine  the  amount  of  the  loan. 

(3)  The  applicant's  liabilities,  both  as  maker  or  endorser 
of  notes. 

249.  Although  a  bank  is  organized  by  individuals,  its 
business  is  of  such  a  nature  that  it  is  subject  to  very  care- 
ful regulation  by  law,  both  as  to  its  organization  and  its 
methods  of  doing  business.  There  are  six  kinds  of  banks, 
viz. : 

(a)  National  banks  are  chartered  by  tlie  federal  govern- 
ment. They  are  authorized  to  issue  money  (bank  notes), 
and  are  limited  as  to  the  kinds  of  loans  they  may  make. 

167 


158  BANKS  AND  BANKING 

(6)  Federal  reserve  banks  are  central  banks  in  the  national 
banking  ^\stem.  They  are  authorized  to  issue  money  (fed- 
eral reserve  notes),  and  most  of  their  business  is  transacted 
with  other  banks. 

(c?)  State  banks  are  organized  under  state  laws ;  in  many 
details  they  are  like  national  banks. 

(^d)  Savings  banks  receive  money  in  small  amounts,  and 
usually  pay  interest  on  deposits. 

(g)  Private  banks  are  companies  or  individuals  doing 
a  banking  business  under  a  private  name. 

(/)  Trust  companies  generally  have   two  departments: 

(1)  a  banking  department  doing  a  general  banking  business ; 

(2)  a  trust  department  which  acts  as  executor  of   estates, 
guardian  of  minors,  etc. 

250.  Banks  receive  for  safe-keeping  valuables  such  as  stock 
certificates,  bonds,  insurance  policies,  and  the  like.  Valu- 
ables of  this  kind  are  usually  kept  in  safety  deposit  boxes 
which  are  rented  to  individuals. 

251.  The  character  of  the  bank  is  indicated  by  its  name, 
as  First  National,  Kent  Savings,  City  Trust  and  Savings, 
First  State,  etc. 

252.  Deposits.  An  individual  may  deposit  funds  in  a  bank 
by  (1)  opening  an  account,  and  (2)  taking  out  a  certificate 
of  deposit. 

(1)  A  checking  account  is  one  in  which  the  funds  on  de- 
posit are  subject  to  withdrawal  by  check. 

The  depositor  fills  out  a  deposit  slip,  and  the  amount  de- 
posited is  entered  by  the  bank  clerk  (teller)  in  the  bank  or 
pass  book  carried  by  the  depositor.  This  entry  is  a  record 
of  the  transaction  for  the  depositor.  The  bank,  however, 
opens  an  account  for  the  depositor  in  its  ledger,  and  keeps  a 
daily  record  of  deposits  and  withdrawals.  The  amount  on 
deposit  is  called  the  depositor's  balance. 


BANKING 


159 


Deposit  Slip 
FIDELITY   TRUST   COMPANY 

DEPOSITED    BY 

Canj  Bros. 


St.  Louis,  Mo., 


Mar. 


1915 


PLEASE 

LIST 

EACH 

CHECK    SEPARATELY 

Dollars 

Cents 

Currency 

121 

Gold 

Silver 
A.  a  Co. 

CHECKS 

31.26 

13 

20 

A.  a  Co. 

20.15 

M.  L.  T. 

108.26 

F.  Hall 

7.60 

167 

Total 

27 

801 

47 

A  savings  ac- 
count is  one  in 
which  the  funds  on 
deposit  draw  inter- 
est at  an  agreed 
rate  (usually  3  or 
4%),  and  are  sub- 
ject to  withdrawal 
only  on  presenta- 
tion of  the  pass 
book. 

Accompanying  is 
a  form  of  pass  book 
used  in  opening  a 
savings  account  : 

It  will  be  no- 
ticed that  with- 
drawals as  well  as 


The  Security  Savings  Bank  Co. 

Withdrawals 

Deposits 

Balance 

L^^. 

f 

Jlc 

oo 

Sl 

-)  o 

fV" 

i<r 

2  i 

?  0 

(l.^ 

/ 

3. 

ro 

^ 

/ 

fv  Y     ly 

^.f: 

JL^ 

// 

L^ 

ro 

///^ 

L^ 

7 

fn( 

1  o 

(T^ 

/ 

iy\C  - 

„ 

/o 

.5fJ 

ro 

.W^ 

S 

,r( 

70 

/ 

160 


BANKS  AND  BANKING 


Columbus.  Ohio. 
THIS  IS  TO  CERTIFY 

THAT  THE  SUM  OF 


HAS  BEEN  DEPOSITED  WITH  THIS  BANK 
PAYABLE  TO  THE  ORDER  OF 


ON  THE  DELIVERY  AND  SURRENDER  OF  THIS 
CERTIFICATEPROPERLY  ENDORSED  WITH  UJ<- 
MATURED  COUPONS  IF  ANY 
THIS  CERTIFICATE  BEARS  INTEREST  FROM  ITS 
DATE  ATTHE  RATE  OFTHREEPERCENTUM  PER 
ANNUM,  PAYABLE  QUARTERLY  BY  THE  DE- 
LIVERY AND5URRENDER  AS  THEY  BECOME 
DUE  OF  THE COUPONSi  PAYABLE  TO  BEARER) 
HERETO  ATTACHED 
THE  PRINCIPAL  SUM  OF 

ONE   HUNDRED  DOLLARS 

/S  DUE  AND  PA  YABU  WiTHQUT  NOTICE  AT  THE 

MATURITY  DATE  or  ANY  COUPON.  OR  AT  ANY  OTHEH 

TIME  WITHOUT  INTEIfEST  FROM  THE  PREVIOUS 

COUPON  DUE  DATE. 

COLUMBUS.O 

THE  OHIO  NATIOHAL  BAHK. 


By       V^ 


Certificate  of  Deposit  and 
Coupon 


deposits  are  entered  in  the  pass 
book.  The  depositor's  balance 
can  be  determined  at  any  time 
by  the  entries.  This  is  not  true 
in  a  checking  account. 

(2)  Certificates  of  deposit. 
Funds  may  be  deposited  in  a 
bank  and  a  certificate  issued 
stating  the  date,  amount,  de- 
positor, and  person  to  whom 
payable. 

Certificates  of  deposit  are 
issued  as  a  convenience  to  those 
who  wish  to  get  interest  on 
their  money  and  still  be  able 
to  get  it  from  the  bank  on  de- 
mand. They  draw  a  specified 
rate  of  interest,  commonly  from 
3  to.  4  %,  if  the  money  is  left 
in  the  bank  a  specified  time 
(usually  3  mo.  or  more),  in- 
terest ceasing  at  the  end  of 
1  yr.  unless  a  new  certificate 
is  issued. 

The  accompanying  shows  the 
form  of  a  certificate  of  deposit 
on  which  the  interest  is  pay- 
able every  3  mo.  by  coupon. 


253.  Withdrawals.  Funds  are  withdrawn  from  a  bank 
(1)  by  check,  if  a  checking  account ;  (2)  by  presenta- 
tion of  the  pass  book  and  by  signing  a  receipt,  if  a 
savings  account;  (3)  by  the  surrender  of  a  certificate  of 
deposit. 


BANKING  161 

The  following  is  the  form  of  check  commonly  used  : 


'"^ 


^9k_ 


I  AUi — ^  3  /  K«MtT  Worth.  Ti.-.va.s      /^-fco    "7- o imO- 


I^O 


/•.^^M...>&^,  (Ely^  CHIti^^na  ^aimnal  iBank 


AmtiltimitHi 

Total 
A»iHlii$Clutt 


Bnl  rant  font  |53  I  \i 


3jif_r_\ 


X/a-rrv**^  (Jryp*,^ 


The  "  stub  "  of  the  check  is  for  the  convenience  of  the 
depositor  in  keeping  a  record  of  his  transactions  with  the 
bank.  When  would  the  balance,  as  shown  on  the  stub, 
differ  from  that  in  the  bank's  ledger  ? 

254.  Unless  withdrawn,  interest  is  allowed  on  savings  de- 
posits twice  a  year,  on  Jan.  1  and  on  July  1 ;  thus  com- 
pound interest  is  paid.  No  interest  is  paid  on  parts  of  a 
dollar,  nor  usually  on  any  money  not  left  during  the  entire 
interest  period. 

Savings  banks  may  demand  30  days'  notice  of  the  with- 
drawal of  funds. 

1.  In  the  savings  account  of  Louis  Cooper,  p.  159,  enter 
the  proper  interest  due  him  at  3%  on  July  1,  1918,  and  on 
Jan.  1,  1914,  and  compute  his  balance  on  Feb.  6,  1914. 

2.  The  City  Railway  and  Light  Co.'s  balance  in  the 
Fourth  National  Bank  on  Dec.  9  is  134,786.49.  The  com- 
pany makes  a  deposit  of  i  18,726.12,  and  draws  a  check  for 
its  weekly  pay  roll  for  $20,112.47.  What  is  the  company's 
balance  at  the  opening  of  the  bank  on  Dec.  10  ? 

3.  What  is  the  value  of  a  certificate  of  deposit  for  $350 
dated  Feb.  23,  1912,  bearing  interest  at  3%,  on  Dec.  23, 
1912?     What  is  its  value  on  June  15, 1912?     June  15, 1913? 

255.  An  indorsement  is  anything  written  on  the  back  of 
a  commercial  paper,  which  refers  to  the  paper  itself. 

BUS.    ARITII.  —  11 


162  BANKS  AND  BANKING 

256.  Checks,  certificates  of  deposit,  and  other  forms  of 
commercial  paper  may  be  transferred  from  one  person  to 
another  by  indorsement,  unless  drawn  to  the  contrary  ;  they 
are  called  negotiable  paper.  The  omission  of  the  words  "  or 
order,"  or  "to  the  order  of,"  makes  paper  nonnegotiable. 

Such  indorsements  may  read  :  "  Pay  to  the  order  of ," 

"  Pay  to or  order,"  "  Pay  to  bearer,"  etc.  The  follow- 
ing indorsements,  supposed  to  be  written  on  the  back  of  the 
check  on  p.  161,  show  (on  the  left)  the  indorsement  used  in 
cashing  the  check  ;  (on  the  right)  the  indorsement  used  in 
transferring  the  money  to  Charles  Elwert. 


Henry  Hawkins 


Pay  to  Charles  Elwbrt 
or  order 

Henry  Hawkins 


257.  Postal  savings  banks  have  been  established  by  the 
United  States  government  at  certain  post  offices. 

Postal  savings  certificates  are  issued  in  denominations  of 
f  1,  12,  85,  f  10,  820,  and  150,  each  bearing  the  name  of  the 
depositor  and  other  necessary  information.  Deposits  up  to 
8100  monthly  are  allowed  to  any  one  person. 

Interest  at  2  %  annually  is  paid  on  each  certificate  left  on 
deposit  for  a  full  year.     Compound  interest  is  not  allowed. 

United  States  bonds,  bearing  interest  at  2J%,  to  any 
amount  not  exceeding  8500  to  one  person,  will  be  issued  to 
a  depositor  upon  surrender  of  certificates. 

258.  Loans  and  discounts.  Banks  lend  money  on  notes, 
the  payment  of  which  is  secured  by  some  valuable  assigned 
as  security  or  collateral. 

Loans  are  made  on  ''collateral  notes,"  on  "judgment 
notes,"  and  the  like.  Forms  of  notes  differ  for  different 
kinds  of  business. 


LOANS  163 

Notes  may  be  secured  in  the  following  ways : 

1.  By  the  indorsement  of  one  or  more  persons  who  thus 
become  liable  for  payment. 

2.  By  the  deposit  of  collateral. 

3.  By  the  mortgaging  of  property. 


'H^.-y'f    ^^yv  Ji^_ 


^itt^    "^^^yo      yy/^^yi^y^f^//:^^yy^pfi>iZ^J/^//^j^^ 


PROTEST  WAIVED 


Q)zye ^^^^^^^^Ld  Jj^mi^  ^^/    ^^'^^    ^^^-y 


Form  of  Note 

260.  Loans  may  be  classified  as  follows : 

{a)  Investment  loans,  made  upon  collateral  security  which 
can  readily  be  turned  into  cash. 

(5)  Industrial  loans,  made  to  manufacturers,  merchants, 
and  farmers  for  discounting  bills,  extending  trade,  moving 
crops,  etc. 

(c)  Capital  loans,  made  to  manufacturers  and  merchants 
who  want  permanent  capital  for  starting  a  business  and  ex- 
pect to  repay  the  loans  from  the  earnings  of  the  business. 

(c?)  Mortgage  loans,  made  usually  on  real  estate  as 
security. 

261.  Most  banks  make  short-time  loans,  the  notes  usually 
falling  due  in  30,  60,  or  90  days;  or  demand  loans  which 
may  be  called  in   (payment  demanded)  at  any  time. 

Long-time  loans  are  made  by  savings  banks  and  by  trust 
companies.  Most  of  the  money  lent  on  mortgage  security 
is  lent  b}^  individuals  or  by  insurance  companies. 


164  BANKS  AND  BANKESTG 

262.  Organizations  known  as  Building  and  Loan  Associa- 
tions make  loans  on  real  estate,  especially  for  building  pur- 
poses. In  order  to  secure  such  a  loan  one  must  become  a 
stockholder  in  the  association,  the  payments  for  stock  and 
the  repayment  of  the  loan  being  made  in  weekly  or  monthly 
installments. 

263.  The  date  on  which  a  note  or  obligation  becomes  due 
and  payable  is  called  the  date  of  maturity. 

BANK   DISCOUNT 

264.  Bank  discount  is  an  amount  deducted  from  the  face 
of  a  note  as  a  consideration  for  the  use  of  the  money  before 
matuiity. 

If  the  note  bears  interest,  the  discount  is  deducted  from 
the  face  of  the  note  plus  the  interest. 

265.  The  proceeds  is  the  amount  left  after  the  discount 
has  been  deducted. 

266.  Time  of  discoimt  is  the  actual  time  from  the  date  the 
note  is  discounted  to  the  day  of  maturity. 

267.  Interest  is  figured  by  calendar  years,  months,  or 
days,  according  to  the  wording  of  the  note  or  draft.  Bank 
discount  is  reckoned  on  actual  time  for  parts  of  a  year,  not 
counting  the  day  of  discount. 


Arkansas,  Mississippi,  Oklahoma,  Soutli  Dakota, 
South  Carolina,  and  Texas  allow  3  days  of  grace  beyond 
the  date  of  maturity  on  notes  and  drafts;  Massachusetts, 
Minnesota,  New  Hampshire,  and  Rhode  Island  on  sight 
drafts.     (See  Exchange,  p.  201.) 

Note.     Problems  in  bank  discount  are  based  upon  percentage  and 
common  interest    'No  days  of  grace  are  considered  in  this  text. 


BANK  DISCOUNT  165 

EXERCISES 

1.    Find  the  bank  discount  and  proceeds  of  the  following 
note,  which  was  discounted  Jan.  6,  1913,  at  8%. 


^^Tz^^^^y&rada-       "^^  >  /^'-^      J^_ 


C/^t^^v^  -rr.t-,.jt-^        c^/4Cfr(////eYtfiiikMffmfe//^aHiue^/raef'/^ idL-  ^om/Je^/r^/i/zy 


/<'/%/?.{m^z^  /y '*^'^^"*^ — — 


^-"/^-   ^^-y    -^ "^^^^  ^-7^^.    '^^^  "    -^  •  Q)^h£m 


PROTEST  WAIVED^^,^^ 


Solution 
Nov.  1,  1912  +  4  mo.  =  March  1,  1913,  date  of  maturity. 

Time  of  Discount  Iktf.kest 

31  $5680.10,  principal 

6  56.804,  interest  60  da.      ,  ^  ^^ 


:| 


25  da.  in  Jan.  56.804,  interest  60  da 

29  da.  in  Feb.  $5794.01,    amount  to  be  discounted 

1  da.  in  March. 
55  da. 

$57.94,    discount  for  60  da.  at  6% 

4.828,  discount  for    5  da.  at  6% 

53.112,  discount  for  55  da.  at  6% 

17.704,  discount  for  55  da.  at  2% 

70.82,    discount  for  55  da.  at  8% 

$5794.01  -  $70.82  =  $5723.19,  proceeds. 

Find  the  discount  and  proceeds  of : 

2.  $1500  with  interest  at  4%  for  6  mo.  from  April  10, 
discounted  June  8  at  6%. 

3.  8875  with  interest  at  6%  for  90  da.  from  Jan.  3,  dis- 
counted Feb.  5  at  7%. 


166 


BANKS  AND  BANKING 


4.  83100  without  interest  for  1   yr.    from  July  7,  1914, 
discounted  Dec.  10,  1914,  at  6%. 

5.  14750  with   interest  at  41  %  for    120  da.   from    June 
11,  discounted  Aug.  1  at  7  %. 

269.    Hankers  make  use  of  a  table  for  finding  tlie  number 
of  days  between  dates. 

Time  Table 


From 

Jan. 

Feu. 

Mar.  Apr. 

May 

To 
JiNE  Jilt 

Acq.  Sept. 

Oct. 

Nov.  Dec. 

Jan. 

365 

31 

69 

90 

120 

151 

181 

212 

243 

273 

304 

3:^ 

Feb. 

334 

365 

28 

59 

89 

120 

150 

181 

212 

242 

273 

303 

Mar. 

306 

337 

366 

31 

61 

92 

122 

153 

184 

214 

245 

275 

Apr. 

275 

306 

334 

365 

30 

61 

91 

122 

153 

183 

214 

244 

May 

245 

276 

304 

335 

365 

31 

61 

92 

123 

163 

184 

214 

June 

214 

245 

273 

304 

334 

365 

30 

61 

92 

122 

153 

183 

July 

184 

216 

243 

274 

304 

335 

365 

31 

62 

92 

123 

153 

Aug. 

153 

184 

212 

243 

273 

304 

334 

365 

.31 

61 

92 

122 

Sept. 

122 

153 

181 

212 

242 

273 

303 

334 

365 

30 

61 

91 

Oct. 

92 

123 

161 

182 

212 

243 

273 

304 

335 

365 

31 

61 

Nov. 

61 

92 

120 

151 

181 

212 

242 

273 

304 

334 

.365 

30 

Dec. 

31 

62 

90 

121 

151 

182 

212 

243 

274 

304 

335 

305 

Explanation  of  Table.  From  Jan.  10  to  Jan.  10  is  365  da.; 
from  Jan.  10,  1912,  to  Jan.  24,  1913,  is  36.5  da.  +  14  da. ;  from  June  6 
to  Nov.  30  is  177  da.  (24  +  153). 

Note.  When  banks  discount  a  paper,  they  often  charge  for  their  serv- 
ices a  certain  per  cent,  ranging  from  ^^  %  ^o  i  %,  on  the  face  of  the  paper, 
or  the  face  phis  the  interest;  there  is  usually  a  minimum  charge  of  10^-. 
This  charge  is  called  collection.  The  bank  discount  plus  the  collection 
charge  is  the  total  charge. 


BANK  DISCOUNT 


167 


EXERCISES 


Find  the  bank  discount  and  proceeds  on  the  following. 
Use  the  table  (§  269)  for  finding  the  number  of  days. 


Face 

Date 

Date  Due 

Kate 

Date 

Discounted 

Ratk 

Discounted 

1. 

1  700 

1/  2/13 

7/  2/13 

5% 

3/  4/13 

6% 

2. 

1460 

9/  3/11 

11/  3/11 

6 

10/21/12 

6 

3. 

1500 

7/  5/12 

1/  5/13 

7 

10/12/12 

6 

4. 

50 

10/31/12 

11/30/12 

6 

11/  5/12 

^ 

5. 

3146.75 

1/24/13 

5/24/13 

6 

3/20/13 

8 

6. 

8154.09 

2/27/13 

10/27/13 

4 

6/12/13 

6 

7. 

321.44 

3/15/13 

4/15/13 

5 

4/10/13 

7 

8. 

750 

5/22/13 

8/22/13 

H 

7/31/13 

^ 

9. 

1000 

1/2/12 

1/  2/14 

6 

11/24/13 

6 

10. 

150 

2/  3/12 

2/  3/13 

8 

1/  6/13 

7 

11.    The  following  note  was  discounted  Jan.  1,  1913,  at 
fo  ;   collection,  ^  %,  computed  on  the  face  of  the  note.     Find 
the  bank  discount  and  proceeds  after  allowing  for  collection. 


6 


$3259  Nashville,  Tenn.,  Dec.  1,  1912. 

Sixty  days  after  date,  for  value  received,  we  promise  to  pay  Wm.  A. 
Pierson  or  order, 

Thirty-two  hundred  fifty-nine  no/100  dollars,  at  the  Traders'  National 

Bank,  in  Nashville,  Tenn.,  with  interest  at  the  rate  of  eight  per  cent  per 

annum  after  maturity  until  paid. 

Carroll  Bros,  and  Co. 


12.  Find  the  proceeds  on  a  3  mo.  note  for  8175,  interest 
at  8  %  from  Oct.  5,  discounted  Oct.  16  at  10  %  ;  collec- 
tion, 1%. 

13.  A  90-da.  draft  for  f!350  was  discounted  Jan.  3,  1913, 
the  day  of  acceptance,  at  6%;  collection,  ^%.  Find  the 
proceeds. 


168  BANKS  AND  BANKING 

PRESENT   WORTH   AND    TRUE   DISCOUNT 

270.  The  present  worth  of  a  debt  is  the  sum  which,  put  at 
interest,  will  produce  the  value  of  the  debt  at  maturity. 

271.  The  true  discount  is  the  difference  between  the 
amount  due  at  maturity  and  the  present  worth. 

Note.  Bank  discount  is  rapidly  replacing  present  worth  and  true 
discount. 

1.  Find  the  present  worth  and  true  discount  of  a  debt 
of  $500,  due  in  6  mo.,  if  the  rate  of  discount  is  6%. 

il,  with  int.  at  6%  for  6  mo.,  will  amount  to  il.03. 

If  'f  1  amounts  to  $1.08  in  6  mo.  at  6%,  it  will  take  as 
many  dollars  to  amount  to  1500  in  that  time  as  $1.03  is  con- 
tained in  1500,  or  485.44. 

Then  $485.44  is  the  present  worth. 

$500  -  $485.44  is  the  true  discount,  $14.56. 

Find  the  present  worth  and  true  discount  of : 

2.  $1700  for  3  mo.  at  4% 

3.  $2500  for  4  mo.  at  5% 

4.  $5000  for  10  mo.  at  6% 

5.  $900  for  2  yr.  and  6  mo.  at  8% 

6.  What  is  the  difference  between  true  discount  and 
bank  discount  on  a  note  for  $1000  for  8  mo.  at  8%? 

7.  Find  the  simple  interest,  true  discount,  and  bank  dis- 
count on  a  note  for  $8000  for  6  mo.  at  6%. 

8.  A  dealer's  price  on  an  automobile  is  $1200,  4  mo. 
time,  or  $1150  cash.  At  what  per  cent  does  he  figure 
money  ? 

9.  A  bill  of  goods  is  invoiced  at  $2500  on  3  mo.  credit. 
For  how  much  must  a  note  be  drawn  with  interest  at  6  %  to 
cancel  the  debt? 


PARTIAL  PAYMENTS 


169 


10.    What  note  at  6%  interest   must  be  given    March  1 
to  cancel  the  following  bill  at  maturity? 

New  York,  N.Y.,  2/18/12. 


C.  H.  Garrjson 

Detroit,  Mich.                                                              Salesman  C.  H. 

Order  taken  8/30. 

In  account  with 

2/10,  net  60 

March  1  dating            PHILLIPS^ONES   COMPANY 

0  Ul 

3         doz.    @    4.50  each 

0U3 

1  6/12       "       @    4.50    " 

898 

4  6/12       "       @    4.50    " 

898  B 

1  6/12       "       @    4.25    " 

BR  H91 

1  3/12       "       @    8.50    " 

SEl 

1  9/12       "       @    8.50    " 

B  VC61 

1  3/12       "       @    8.50    " 

Total 

PARTIAL   PAYMENTS 

272.  Partial  payment  is  part  payment  on  a  note,  draft,  or 
other  form  of  obligation. 

When  a  payment  is  made,  an  indorsement  is  entered  on  the 
back  of  the  paper,  somewhat  after  the  following  form : 

Rec'd  on  the  within  note 
Jan.  1,  1914,  150 
March  2,  1914,  .^75 

Note.  The  ordinary  practice,  especially  with  banks,  is  to  take  sepa- 
rate notes  for  whatever  payments  are  agreed  upon  at  the  time  the  loan  is 
made.  Thus,  if  a  borrower  wishes  to  borrow  ^150  for  3  mo.,  and  repay 
f  50  a  month,  the  bank  would  probably  take  3  notes  for  $  50  each,  one 
due  in  30  da.,  one  in  60  da.,  and  one  in  90  da. 

273.  The  two  methods  in  general  use  in  computing  partial 
payments  are  the  United  States  Rule  and  the  Merchants' 
Rule. 


170 


BANKS  AND  BANKING 


274.  The  United  States  Rule  is  authorized  by  the  United 
States  Supreme  Court,  and  is  used  when  the  partial  pay- 
ments are  made  on  interest-bearing  notes  having  1  j^r.  or 
more  to  run. 

(a)    Interest  must  not  be  paid  on  interest.  ' 
(6)    Accrued  interest  must  be  paid   before  the  payment 
can  reduce  the  amount  of  the  debt. 

1.  What  was  the  balance  due  on  a  note  for  82000  dated 
June  10,  1911,  to  run  1  yr.  with  interest  at  6%,  the  fol- 
lowing payments  having  been  made:  Aug.  3,  1911,  1500; 
Dec.  15,  1911,  $25;  Feb.  3,  1912,  $500?     (Compound  time 

is  always  used.) 

Solution 

Face  of  note $  2000. 

Int.  from  June  10,  1911,  to  Aug.  3,  1911 17.67 

Amount  due  Aug.  3,  1911 2017.67 

Payment  Aug.  3,  1911 500. 

Balance  due  Aug.  3,  1911 1517.67 

Int.  from  Aug.  3,  1911,  to  Dec.  16,  1911    .     .     .     .   $33.39 

As  this  amount  (833.39)  exceeded  the  amount 
of  the  payment,  int.  and  payment  must  be  carried 

over  to  the  next  payment 

Int.  from  Dec.  15,  1911,  to  Feb.  3,  1912     ....     12.14 

Total  int.  due 45..53 

Amount  due  Feb.  3,  1912 1663.20 

Total  payment  (825 +  $500) 525. 

Balance  due  Feb.  3,  1912 1038.20 

Int.  from  Feb.  3,  1912,  to  June  10,  1912 12.98 

Amount  due  at  settlement 81060.18 

Find  the  balance  due  on  each  of  the  following  notes  : 


Datk 

Face 

TiMK  TO  Run 

Rate 

Payments 

2. 
3. 

Sept.  1,  1909 
Feb.  5,  1900 

$10000  • 
82000 

4yr. 
2yr. 

6% 
4% 

March  1,  1910,  8300 
Dec.  1,  1910,  850 
Junel,  1911,  8400 

May  1,  1900,8200 
Aug.  1,  1901,  8  10  _ 

PARTIAL  PAYMENTS 


171 


275.  The  Merchants'  Rule,  while  not  a  strict  rule  of  law, 
is  generally  used  when  the  interest-bearing  note  runs  1  jr. 
or  less. 

(a)    The  note  bears  interest  until  date  of  settlement. 

(6)  Each  payment  bears  interest  from  its  date  until  date 
of  settlement. 

Note.  Some  business  men  use  exact  time,  while  others  use  compound 
subtraction. 

1.  Face  of  note,.ilOOO;  time,  9  mo.  from  Jan.  1;  rate, 
6%.  Indorsements:  Feb.  1,  1100;  June  1,  $200.  What 
amount  was  due  at  maturity?     (Compound  time.) 

Condensed  Form  of  Solution 


Date 

Face 

'JiME 

Kate 

Interest 

Amount 

Jan.  1 

flOOO 

9  mo. 

6% 

145  00 

.|  1045 

Feb.  1 

100 

8  mo. 

0% 

4.00 

$104 

June  1 

200 

4  mo. 

«% 

4.00 

204 
Balance  due  787 
1 1045        f 1045 

Find  the  balance  due  on  each  of  the  following,  using  com- 
pound subtraction  to  find  the  time  in  the  2d  and  3d,  and 
exact  time  in  the  4th  and  5th. 


' 

Date 

Face 

Time 

Eate 

Indorsements 

2. 

Feb.  1,  1912 

$4000 

10  mo. 

6% 

April    3,  1912,  $500 
June     1,  1912,    100 
Oct.    10,  1912,    200 

3. 

Jan.  25,  1910 

1500 

7  mo. 

7% 

Feb.   18,  1910,    150 
July     2,  1910,    350 

4. 

Aug.  9,  1908 

850 

5  mo. 

6% 

Sept.  28,  1908,      75 
Nov.     5,  1908,      60 
Jan.     1,  1909,    100 

5. 

Dec.  10,  1903 

2000 

9  mo. 

5% 

Jan.    20,  1904,    200 
Feb.   25,  ie04,    300 

172 


BANKS  AND  BANKING 


MISCELLANEOUS   PROBLEMS 
Group  1 

1.  From  the  equation  PRT=  /,  find  R, 

2.  By  applying  the  formula,  find  /  in  the  following  : 

PR  T 

$260.  6%  lyr. 

720.  4%  6  mo. 

8400.  6%  3  mo. 

568.72  7%  90  da. 

85.60  8%  4  mo. 


3.    By  the  cancellation  method  find  the  interest  on  the 


following 


$98.60  for  72  da.  at  6% 
$321.05  for  90  da.  at  5% 
$426.17  for  35  da.  at  7% 
$1260.09  for  63  da.  at  6% 
$815.  for  3  mo.  at  8% 


4.    By    the 

following : 


60-da.    method    find    the    interest    on    the 

$621.50  for  4  mo.  at  6% 
$283.17  for  5  mo.  at  5% 
$12620.70  for  lyr.  at  4J% 
$84.62  for  75  da.  at  3%" 
$161.13  for  112  da.  at  3J  % 


5.    By  the  6%  method  find  the  interest  on  the  following 

$378.50  from  Feb.  2,  1913,  to  April  10,  1913,  at  6% 

$216.06  from  11/3/12  to  2/1/13  at  8% 

$7615.83  from  Oct.  23,  1912,  to  Jan.  13,  1913,  at  5% 

$70  from  1/3/13  to  4/19/13  at  7% 

$169.69  from  1/15/13  to  2/28/13  at  4  % 


MISCELLANEOUS  PROBLEMS  173 

6.  By  the  interest  table,  p.  149,  find  the  interest  on  the 
folio wmg  :       ^^^^^  ^^^  g  ^^^  g  ^^^  ^^  ^1  ^^ 

1300  for  3  mo.  at  6% 
f  279  for  1  mo.  15  da.  at  5% 
11628  for  1  yr.  2  mo.  11  da.  at  5^% 
$65  for  36  da.  at  7% 

7.  Find  the  exact  interest  (p.  151)  on : 

11427  for  48  da.  at  6% 

1216.60  for  37  da.  at  6^% 

i98.54  for  3  mo.  12  da.  at  5  % 

1627.43  for  1  mo.  15  da.  at  41% 

f  13261.82  for  1  yr.  2  mo.  27  da.  at  7  % 

8.  Find,  by  the  most  convenient  method  for  each,  the 
interest  on  the  following  : 

#3726.81  from  April  5,  1911,  to  June  3,  1913,  at  6% 
1281.54  from  Oct.  13,  1912,  to  Jan.  5,  1913,  at  7% 
$2200  from  July  3,  1910,  to  Aug.  6,  1914,  at  8% 
•$75  for  7  mo.  8  da.  at  2^% 
$125  for  9  mo.  22  da.  at  4% 

9.  A  man  lent  X  2159  5s.  Qd.  at  6%.  Find  the  interest 
yearly. 

10.    How  much  money  must  I  invest  at  5%  in  order  to 
receive  a  semiannual  income  of  $1268.50? 

Group  2 

1.  A  man  builds  a  house  costing  $3200.  He  pays  $1400 
cash  and  gives  three  equal  notes  for  the  balance  due,  payable 
in  1,  2,  and  3  yr.  respectively,  with  interest  at  5%.  If  he 
pays  all  interest  due  at  the  end  of  each  year,  what  amount 
does  he  pay  at  the  end  of  each  year  in  paying  off  the  in- 
debtedness ? 


174  BANKS  AND  BANKING 

2.  A  merchant  bought  a  bill  of  goods  on  the  following 
terms :  3  %  cash,  net  90  da.  At  what  rate  can  he  afford 
to  borrow  .money  in  order  to  pay  cash  ? 

3.  A  bank  pays  3%  interest  on  deposits  amounting  to 
11628,453.27;  its  loans  average  $1,462,817.61  at  5%,  and 
11,316,478.55  at  6%.     What  is  the  bank's  yearly  profit? 

4.  A  city's  bonded  debt  is  $1,031,000.  At  4%,  what 
interest  does  it  pay  annually  ? 

5.  A  merchant  bought  #5000  worth  of  goods,  terms 
net  60  da.  At  the  end  of  the  60  da.  he  had  sold  75% 
of  the  goods  at  a  profit  of  20  %  on  the  cost,  and  the  rest  of 
them  at  cost.     How  much  did  he  gain  ? 

6.  A  gave  his  60-da.  note  to  a  bank  for  $200  at  6% 
interest.  If  the  bank  deducts  the  interest  in  advance,  how 
much  does  he  receive  for  the  note  ? 

7.  On  April  1, 1910,  A  bought  a  bill  of  goods  amounting 
to  $1500.  He  gave  his  note  for  the  amount,  interest  at  5%. 
How  much  did  he  pay  at  settlement,  Nov.  15,  1910  ? 

8.  A  company  bought  1000  bales  of  cotton  at  $11.91 
per  bale,  giving  a  30-da.  5J  %  note  in  payment.  How  much 
interest  did  it  pay  at  maturity  ? 

9.  A  farmer  bought  an  80-acre  farm  for  $50  per  acre. 
He  paid  $800  down,  and  gave  four  equal  notes  for  the 
balance  due,  payable  in  1,  2,  3,  and  4  yr.  respectively, 
interest  at  6%,  payable  annually.  How  much  did  he  pay 
at  the  end  of  each  year  until  all  the  notes  were  paid  ? 

10.  A  railroad  company  buys  1000  gondola  cars  at  $1000 
each,  giving  in  payment  20  series  of  50  notes  to  each  series, 
all  dated  July  1,  1913.  One  series  matures  at  the  end  of 
each  6  months,  and  all  bear  interest  at  6%  per  annum  from 
date,  interest  payable  semiannually.  What  amount  must 
the  company  pay  at  the  end  of  the  first  6  months  ?  at  the 
end  of  the  second  6  months  ? 


MISCELLANEOUS  PROBLEMS  175 

Group  3 

1.  A  city  authorizes  the  issuance  of  1350,000  10-yr.  bonds 
at  4%  for  the  purpose  of  building  a  viaduct.  What  amount 
must  be  paid  to  a  sinking  fund  earning  3|  %  in  order  to 
redeem  the  bonds  at  maturity?     (Use  table,  page  156.) 

2.  A  depositor  has  $  1000  in  the  savings  bank  at  3  % 
interest.  He  draws  out  the  money  and  buys  a  lot  which  he 
sells  6  mo.  later  for  i)1100.  If  he  pays  il5  taxes  on  the 
lot,  and  #20  selling  commission,  what  per  cent  does  he  make 
on  his  $1000  in  excess  of  what  it  would  have  earned  for 
him  if  left  in  the  bank? 

3.  An  electric  light  company  borrows,  on  a  5-J%  bond 
issue,  #100,000  for  extensions  and  improvements.  What 
interest  does  it  pay  annually  on  the  debt,  and  what  amount 
must  it  deposit  with  the  trustee  of  the  sinking  fund  earning 
4|  %  to  redeem  the  bonds  in  5  yr.  ? 

4.  What  is  the  difference  between  a  checking  and  a 
savings  account  at  a  bank  ? 

5.  The  bank  clearings  in  New  Orleans  on  a  certain  day 
were  11,841,109,  as  against  11,524,060  for  the  corresponding 
day  the  year  before.      What  was  the  percentage  of  increase  ? 

6.  A  coupon  certificate  of  deposit  for  |600,  drawing 
interest  at  3%,  is  dated  Oct.  28,  1912.  If  all  the  coupons 
are  left  attached,  what  is  the  value  of  the  certificate  on 
Aug.  3,  1913  ? 

7.  A  cotton  dealer  sold  700  bales  of  cotton  at  $12.08 
per  bale,  and  accepted  in  payment  a  90-da.  note  bearing 
interest  at  5%.  If  he  discounts  the  note  at  his  bank  at 
5%,  how  much  does  he  receive  for  it  ?  / 

8.  A  bank  discounts  a  60-da.  draft  at  6%,  allowing  5 
da.  for  collection  and  return.  If  the  face  of  the  draft  is 
$675.84,  what  are  the  proceeds,  there  being  no  charge  for 


176  BANKS  AND  BANKING 

collection  ?     (Time  for  collection  and  return  must  be  added 
to  time  of  draft.) 

9.  A  jobber  buys  goods  from  a  manufacturer  to  the 
amount  of  r^ 27,600,  and  gives  his  note  in  payment  for  4  mo. 
at  5%.  The  jobber  sells  the  goods  to  customers  at  a  profit 
of  12  J  %  on  the  cost,  taking  60- da.  6%  notes  in  payment. 
At  the  end  of  60  da.,  receiving  the  money  on  his  customer's 
notes,  he  discounts  his  note  to  the  manufacturer  at  6  %. 
What  is  his  profit  on  the  transaction  ? 

10.  A,  holding  B's  7  %  60-da.  note  for  1 1200,  has  it  dis- 
counted at  the  bank  for  the  full  time  at  6%.  At  the  end  of 
30  da.,  having  idle  funds,  A  buys  the  note  back  from  the 
bank,  discounting  it  at  6%.  What  net  amount  does  A 
receive  in  interest  ? 

Group  4 

1.  A  retail  merchant  sold  out  a  stock  of  goods  and  in- 
vested 70  %  of  the  money  in  a  farm  which  paid  him  a  yearly 
rental  of  $600.  If  the  rate  of  income  on  his  farm  invest- 
ment is  8J  %,  for  what  amount  did  he  close  out  his  stock  ? 

2.  The  profits  of  a  manufacturing  business  the  first  year 
are  40%  of  the  capital  employed;  75%  of  this  gain  is  rein- 
vested in  the  business  for  the  2d  year.  The  2d  year 
shows  a  profit  of  45  %  on  the  capital  employed,  and  all  this 
profit  is  allowed  to  remain  in  the  business  for  the  3d  year. 
What  per  cent  of  the  original  capital  does  the  business  start 
with  for  the  3d  year  ?, 

3.  What  rate  of  commission  is  charged  for  selling  goods 
for  f  562.25,  the  net  proceeds  of  the  sale  being  1541.17? 

4.  A  bought  a  bill  of  goods  to  the  amount  of  $640,  terms 
3%/10,  net  30.  In  order  to  secure  the  10-da.  discount  he 
discounted  his  60-da.  note  at  the  bank  at  6%.  Find  the 
face  of  the  note. 


MISCELLANEOUS  PROBLEMS 


177 


5.  Find  the  difference  between  the  simple  interest  and 
true  discount  on  12500  for  90  da.  at  5%.  Find  the  dif- 
ference between  simple  interest  and  bank  discount. 

6.  If  the  John  F.  Price  Co.  accepted  Frank  Mueller's 
60-da.  note  in  payment  of  the  following  bill,  for  what 
amount  could  it  be  discounted  at  the  bank,  interest  being  at 
the  rate  of  6  %  ? 

Sept.  20,  1914. 


Frank  Mueller 
Ogden,  Utah. 


In  account  with 
The   JOHN  F.    PRICE   CO. 


suit 

doz.  hdkfs.  @  2  for  25^ 
pr.  sacks  @  3  pr.  for  $  1 
shirts  @  $1.76  each  . 
ties  @  $  4  per  dozen 


7.  What  is  the  difference  between  the  true  and  bank 
discount  on  1 3000  for  150  da.  at  6  %  ? 

8.  Find  the  balance  due  at  maturity  by  United  States 
Rule  on  the  following  note  : 

Face  of  note,  $3500;  date,  Jan.  10,  1913;  time  to  run,  2 
yr.  6  mo. ;  rate  of  interest,  6  %.  Indorsements  are  as  follows  : 
9/25/13,  1400;  11/1/13,  1500;  2/8/1914,  |200;  6/15/14 
•11000. 

9.  On  his  son's  11th  birthday,  a  man  deposited  in  a 
savings  bank  a  sum  sufficient  to  amount  to  tf  3000  on  the 
son's  21st  birthday.  If  the  bank  credits  4  %  interest  annu- 
ally, how  much  was  deposited  ?     (§  242.) 

10.  Find  the  interest  on  £>  200  10s.  bd.  for  2  mo.  15  da., 
at  6  %. 

BUS.    ARITH.  —  12 


178  BANKS  AND  BANKING 

Group  5 

1.  A  contractor  agrees  to  build  a  bridge  for  f  15000. 
He  employs  15  men  for  120  da.  at  $2  per  day  each,  1 
engineer  for  108  da.  at  $5  per  day,  2  teams  for  123  da. 
at  §4.50  per  day  each.  Materials  are  billed  to  him  at  a 
discount  of  2|-%,  the  bills  calling  for  $^7186.20.  In  order  to 
pay  his  men  promptly,  and  to  discount  his  bills,  the  contrac- 
tor borrows  money  from  the  bank  at  6  %  as  follows :  $  2500 
for  1  mo.,  12500  for  2  mo.,  and  13000  for  3  mo.  His 
surety  bond  for  the  safe  completion  of  his  contract  costs  him 
$225.     What  is  the  profit  on  tlie  contract? 

2.  A  man  borrowed  $50  and  agreed  to  pay  back  $10  a 
month  for  6  mo.  Ignoring  interest  on  the  monthly  pay- 
ments, at  what  rate  does  he  pay  interest  on  the  loan  ? 

3.  A  man  invested  $5000  on  Jan.  15,  buying  stocks 
which  he  sold  later  for  $5300.  He  reinvested  this  amount, 
and  sold  out  on  May  2-4  at  an  advance  of  2  %  on  his  in- 
vestment.    What  rate  of  income  lias  his  money  earned  ? 

4.  A  jobber  gives  a  customer  a  discount  of  10  %  from 
list  prices,  with  an  additional  discount  of  2  %  for  cash. 
What  was  the  amount  of  the  bill  at  list  prices  if  the  cus- 
tomer paid  $  2364.85  cash  ? 

5.  A  bill  for  $2534.20  was  due  a  manufacturer  Jan.  2. 
He  carried  the  account  until  May  15  without  interest.  If 
money  is  worth  5  %,  this  was  equivalent  to  what  discount  ? 

6.  A  farmer  owns  a  farm  worth  $  15000  with  its  stock 
and  implements.     His  accounts  for  a  year   are  as  follows : 

Dr.  Cb. 

$1000,  labor,  self  and  wife         $  1400,  sale  of  wheat 
420,  living  expenses  280,  sale  of  stock 

112,  extra  help  150,  sale  of  corn 

150,  taxes  and  incidentals  321,  sale  of  other  products 

What  rate  of  income  does  the  farm  pay  above  expenses  ? 


MISCELLANEOUS  PROBLEMS  179 

7.  A  man  gave  his  note  Feb.  15,  1909,  for  11250.75,  at 
7  %.  Some  time  afterward  he  canceled  the  note  by  paying 
11354.56  in  full.     What  was  the  date  of  cancellation? 

8.  On  March  29,  1908,  J.  R.  Anderson,  of  Fort  Worth, 
Tex.,  bought  of  Scott  Freeman  42  head  of  cattle  at  f  42.50 
a  head,  and  gave  in  payment  an  8%  90-da.  note  payable  at 
the  Citizens'  National  Bank  of  Fort  Worth,  J.  F.  Baker 
becoming  his  security.      Write  the  note. 

9.  Scott  Freeman  discounted  the  above  note  at  the  bank 
on  April  7  at  6  %.     What  were  the  proceeds  ? 

10.    A  city  contracts  for  paving  as  follows  : 

3000'  brick  paving  on  A  St.,  36'  wide,  at  $1.68  per  square 
yard. 

1600'  asphalt  paving  on  B  St.,  30'  wide,  at  $1.80  per 
square  yard. 

7500'  macadam  paving  on  C  St.,  24'  wide,  and  8"  deep,  at 
$2  per  cubic  yard. 

13800'  curbing  on  C  St.,  at  51  ^  per  foot. 

To  pay  for  the  paving  the  city  issues  $50,000  5-yr.  4% 
bonds.  Any  balance  left  out  of  the  $50,000  after  paying 
for  the  paving  is  to  be  deposited  in  a  bank  at  2^  %,  interest 
to  be  paid  semiannually  and  to  be  applied  to  the  bond 
charges  each  six  months.  What  amount  must  the  city  ap- 
propriate to  meet  the  interest  and  sinking  fund  needs  each 
year  if  the  sinking  fund  earns  3J  %  ? 


TAXES 

276.  Taxes  are  sums  of  money  charged  against  persons  or 
property  for  public  purposes. 

277.  Taxes  are  of  two  kinds,  direct  and  indirect. 

278.  Direct  taxes  are  sums  levied  upon  persons  (income 
tax),  property  (property  tax),  or  business  (license  fee). 

The  nature  of  some  direct  taxes  is  indicated  by  the  name, 
such  as  "  Inheritance,"  "  Corporation,"  "  Income  Tax,"  etc. 

279.  Indirect  taxes  are  duties  levied  upon  imported  goods 
(called  tariffs),  or  licenses  charged  on  the  manufacture  of 
liquor  or  tobacco  products  (called  excise  or  internal  revenue). 

280.  Taxes  are  generally  assessed  and  made  payable  in 
money,  except  road  taxes  which  are  often  made  payable  in 
day's  work. 

The  value  at  which  property  is  assessed  is  determined  by 
officials  called  assessors. 

281.  In  solving  tax  problems  use  tlie  principles  of  per- 
centage. 

The  assessed  valuation  is  the  base. 
The  tax  rate  is  tlie  rate. 
The  tax  is  the  percentage. 

282.  Formulas: 

Assessed  valuation  x  rate  =  tax,  or  BR  =  T. 

T 

Tax  -¥-  rate  =  assessed  valuation,  or  —  =  ^. 

M 

T 

Tax  -^  assessed  valuation  =  rate,  or  —  =  R, 

180 


APPORTIONMENT   OF  TAXES 


181 


283.    The  tax  rate  may  be  expressed  in  two  ways ;  by  a 
per  cent,  as  I^^q  %,  or  by  so  much  on  $100,  as  il.30  per  flOO. 

Find  the  tax  on  property  valued  at  12000  at  a  rate  of  1^  %. 

If  BR  =  T, 

then  12000  x  .012  =  $24,  tax. 

Fill  in  the  missing  parts : 


Valuation 

Tax  Rate 

Tax 

1. 

2 

$   5500 
1   1500 
$  12000 
$  6250 

.0126  0/, 
.014  o/„ 

3. 
4. 
5. 
6. 
7. 
8. 

$    93.75 
$112.62 
$  187.50 
$420. 
$   56.32 

.020/0 

$36000 

.022% 

APPORTIONMENT    OF   TAXES 

284.    Direct  taxes  are  apportioned  in  the  following  way : 
Suppose  the  property  value  in  a  state  is  $2,000,000,000; 
the  valuation  of  X  county  is  $25,000,000,  and  of  the  city  of 
Y  $7,000,000. 

Suppose  also  that  the  amount  of  money  to  be  raised, 
exclusive  of  licenses,  permits,  etc.,  is  $14,000,000  for  state 
purposes.  X  county  must  pay  its  proportionate  part  of 
this  $14,000,000,  or  such  a  part  of  it  as  $25,000,000  is  of 
$2,000,000,000. 

$25000000  25        1 1  ^     .  .u       i.  1  .. 

— = =H%  of  the  whole  amount. 

$2000000000      2000       ^^ 

114,000,000  X  .01|  =  $  175000,   amt.  to   be  raised   by  X 

county. 

Further,  if  $25,000  is  needed  for  county  purposes,  then 

X  county  must  raise  a  total  of  $200,000. 


182  TAXES 

Similarly,  the  city  of  Y,  with  a  valuation  of  $  7,000,000, 

must  raise of  the  amount  to  be  raised  by  the  county, 

25000000  ^  ^ 

or  2^  of  8200,000  =  856000,  Y's  share  of  the  county  tax. 

If  the  city  of  Y  must  raise  844000  for  city  expenses,  its  total 
tax  will  be  856000  +  844000,  or  8100,000  for  all  purposes. 

To  find  the  rate  of  taxation,  divide  8100,000,  the  amount 
to  be  raised,  by  87,000,000,  the  total  valuation  of  the  town's 
property.  ^^^^^^^ 


87000000 


=  1|  %,  the  rate. 


1.  A  property  has  an  assessed  valuation  of  810,000. 
What  is  the  tax  at  the  rate  of  8.001  on  a  dollar? 

2.  If  the  assessed  valuation  is  85700  and  the  tax  rate 
1|%,  what  is  the  tax? 

3.  What  is  the  tax  on  85000  at  the  rate  of  8-80  per  8100  ? 

4.  A  corporation  paid  taxes  as  follows :  a  corporation 
tax  (fee)  of  ^5^  1|  %  on  real  estate  assessed  at  8  37,250,  and 
an  income  tax  of  837.50.     What  was  its  total  tax? 

5.  A  man  paid  8230  taxes  on  real  estate  at  1|%.  At 
what  amount  was  his  property  assessed  ? 

6.  An  owner  paid  8201.31  taxes  on  property  assessed  at 
88750.     What  was  the  rate  of  taxation  ? 

7.  An  estate  pays  to  the  state  87240.60  as  an  inheritance 
tax  at  1.5  %.     On  what  amount  is  the  tax  levied  ? 

8.  The  total  property  valuation  of  a  county  is  833,264,780, 
and  the  amount  to  be  raised  by  taxation  is  8650,000.  What 
is  the  tax  on  property  valued  at  84500? 

9.  A  farmer  owns  property,  real  and  personal,  assessed  at 
85235.  His  poll  tax  is  81,  property  tax  875,  and  he  is 
assessed  84  road  tax.  What  per  cent  of  his  property 
valuation  must  he  set  aside  for  taxes  ? 


INDIRECT  TAXES 


183 


INDIRECT   TAXES 

285.  Customs  or  duties  are  levied  by  the  government  for 
two  reasons : 

1.  For  protection  of  American  industries. 

2.  For  raising  revenue. 

286.  Customs  or  duties  are  of  two  kinds, — specific  and 
ad  valorem. 

287.  A  specific  duty  is  a  fixed  sum  of  money  levied  upon 
each  article  regardless  of  its  value. 

288.  An  ad  valorem  duty  is  a  certain  per  cent  levied  upon 
the  market  value  of  the  article  in  the  countrj^  from  which  it 
is  imported. 

289.  Allowances  for  the  weight  of  boxes,  etc.  (called 
tare),  and  for  leakage  and  breakage,  are  made  before  esti- 
mating duties. 

The  long  ton  of  2240  lb.  is  used  in  reckoning  import  duties. 

290.  A  tariff  is  a  list  of  dutiable  articles  with  their  legal  rate. 

291.  A  free  list  is  a  list  of  articles  on  which  no  duty  is 
charged. 

292.  The  following  t^ble  is  taken  from  the  Tariff  Act  of 
1913. 

Import  Duties 


Ahticle 


Specific  Ditty 


Ad  Valoeem  Duty 


Bicycles 

Butter 

Cotton  cloth,  unbleached 

Cotton  clothing,  ready-made      .     .     . 
Leather  "glac6  "  gloves,  ladies'  14  in. 

long  or  less 

ladies'  17  in.  long 

Oilcloth 

Woolen  clothing,  ready-made    .     .     . 


2^^  per  pound 


$  1  per  dozen 
$1.75  per  dozen 


25% 
30% 


25% 
35% 


184 


TAXES 


293.  To  find  a  specific  duty. 

What  is  the  duty  on  175  doz.  ladies'  gloves,  14  in.  long  ? 
175  X  $1  =  $175,  specific  duty. 

Using  the  rates  given  above,  find  the  duty  on : 

1.  200  doz.  ladies'  leather  gloves,  12  in.  long. 

2.  500  doz.  ladies'  leather  gloves,  17  in.  long. 

3.  1500  lb.  of  butter. 

294.  To  find  an  ad  valorem  duty. 

What  is  the  ad  valorem  duty  on  imported  merchandise, 
valued  at  £  300  10«.,  if  the  duty  is  25  %  ? 

<£300  10«=X300.5. 
$4.8665  X  300.5  =  $1462.38,  value  in  United  States  money. 
I  of  $1462  =  $365.50  ad  valorem  duty. 
Note.     The  duty  is  reckoned  on  the  nearest  dollar. 

Find  the  duty  on  : 

1.  300  yd.  of  oilcloth,  invoiced  at  <£  6  8«.  lOd. 

2.  Woolen  clothing  invoiced  at  <£  510. 

3.  A  merchant  imported  merchandise  valued  at  .£8000. 
The  duty  was  50  %.    What  was  the  total  cost  in  U.  S.  money  ? 

4.  Find  the  total  cost  to  the  importer  of  the  following 
shipment  of  gloves,  the  import  duty  on  ladies'  gloves  being 
$1  per  dozen,  and  on  the  men's  gloves,  $2.50  per  dozen,  the 
freight  being  $18.20. 


No.  AnxicLB 

Price 

Amt. 

Duty 

Total 

140  pr.  14"  ladies' 
170  pr.  men's 

$1.45 
1.10 

• 

Total 
Freight 

Total  cost 

INSURANCE 

295.  Insurance  is  an  agreement  by  one  party,  for  a  con- 
sideration, to  indemnify  (pay)  another  party  in  case  of  loss. 

The  loss  may  be  from  any  cause  stipulated  in  the  agree- 
ment, and  the  different  kinds  of  insurance  take  their  names 
from  the  various  causes.  Fire  insurance  is  insurance  against 
loss  by  fire ;  life  insurance  is  insurance  against  loss  of  life ; 
accident,  against  injury  from  accident ;  etc.  Other  kinds  of 
insurance  are  marine,  burglary,  plate  glass,  automobile,  hail, 
liability,  etc. 

296.  The  agreement  between  the  two  parties  is  called  the 
policy.     The  amount  paid  for  insurance  is  the  premium. 

297.  Fire  and  life  insurance  are  the  most  important ;  and 
a  consideration  of  these  two  kinds  will  furnish  the  general 
basis  for  calculating  any  kind  of  insurance.  Hence,  only 
these  two  will  be  treated  in  this  book. 

FIRE    INSURANCE 

298.  Fire  insurance  covers  loss  or  damage  to  property  by 
fire,  water,  smoke,  and  chemical  extinguishers. 

299.  Two  kinds  of  insurance  are  in  general  use :  valued 
policies  and  open  policies. 

300.  A  valued  policy  states  the  amount  to  be  paid  in  case 
of  loss. 

301.  An  open  policy  leaves  the  amount  to  be  paid  in  case 
of  loss  open  to  evidence.  This  form  of  policy  is  generally 
used. 

185 


186  INSURANCE 

302.  Tlie  value  of  the  policy,  or  the  amount  of  risk  as- 
sumed, is  the  base. 

The  rate  of  premium  is  the  rate. 
The  premiimi  is  the  percentage. 

303.  The  rate  of  premium  is  sometimes  stated  as  a  per 
cent  of  the  amount  insured,  and  sometimes  as  a  certain  rate 
on  each  ilOO  of  insurance. 

304.  To  find  the  premiimi. 

A  house  is  insured  for  'f  3000  at  1^%  premium.  Find  the 
cost  of  insurance. 

11%  of  #3000  =  !^45,  premium. 

Find  the  premium  on  each  of  the  following  policies: 


] 

Faok  of  Policy 

Rati  of  PRRMtuM 

1. 

$  3800 

i% 

2. 

$  5600 

\1o 

3. 

$48200 

\1o 

4. 

#12000 

30^  perl  100 

5. 

$  7400 

mo 

6. 

#60500 

42^  peri  100 

7. 

#18300 

21^  peri  100 

8. 

#51200 

1% 

9. 

#17100 

3J% 

.0. 

#25500 

60/ per  $100 

305.   The  insurable    value   of  buildings  is  roughly  esti- 
mated by  the  following  method : 
Dwellings  from  5^  up  per  cubic  foot. 
Barns  from  2^  to  3^  per  cubic  foot. 
Deduct  one  third  for  depreciation  and  owner's  risk. 


FIRE  INSURANCE  187 

303.  What  is  the  insurable  value  of  a  dwelling  30'  x  25'  x  28', 
estimated  to  have  cost  8^  per  cubic  foot? 

30  X  25  X  28  =  21000  cubic  feet 

SI 

il680 
Less  1      560 

$  1120,     insurable  value. 

307.  The  premium  rate  is  liigher  for  a  short  term  than  for 
a  long;  it  is  called  the  short  rate. 

If  a  policy  is  canceled  by  the  insured,  the  company  will 
return  to  him  the  difference  between  the  premium  paid  and 
the  premium  already  expired,  reckoned  at  the  short  rate. 

If  the  company  cancels  the  insurance,  it  will  return  an 
amount  equal  to  the  premium  for  the  unexpired  time 
reckoned  at  the  regular  rates. 

Short-rate  tables  may  be  secured  from  any  insurance 
company. 

308.  Ordinarily,  an  insurance  company  will  limit  its  liabil- 
ity to  loss  on  any  one  property,  except  in  cases  of  "  preferred  " 
risks,  where  there  is  small  chance  of  loss.  Hence,  it  is  cus- 
tomary to  divide  the  insurance  up  among  several  companies. 
In  such  cases,  any  loss  less  than  the  full  amount  of  the  insur- 
ance is  divided  pro  rata  among  the  companies  interested. 

309.  When  the  policy  contains  a  coinsurance  clause,  the 
company  pays  only  such  part  of  any  loss  as  the  face  of  the 
policy  bears  to  the  value  of  the  property,  or  to  a  stipulated 
per  cent  of  its  value. 

Property  valued  at  $12000  is  insured  for  $8000.  A  loss 
of  $7500  is  sustained.  What  amount  would  be  paid  by  the 
company  if  the  policy  contained  a  coinsurance  clause  ? 

12  0T0  ~  3 

I  of  $  7500  =  $5000,  amount  paid. 
What  amount  would  be  paid  under  an  ordinary  policy? 


188  INSURANCE 

310.    A  stock  of  merchandise  is  insured  as  follows : 

In  Company  A  for  $3000. 

In  Company  B  for  S2000. 

In  Company  C  for  i^  1000. 

What  would  each  company  pay  in  the  event  of  a  loss  of 

^'''''       13000 
2000 
1000 
$  6000,  total  insurance 
f  of  13000  =  f  1500,  amount  Company  A  pays, 
f  of  i3000  =  ilOOO,  amount  Company  B  pays. 
J  of  f  3000  =  I  500,  amount  Company  C  pays. 

EXERCISES 

1.  A  dwelling  30'  x  60'  x  25',  costing  10^  per  cubic  foot, 
is  insured  for  5  yr.  at  a  rate  of  il.35  per  1 100.  Find  the 
insurable  value  and  the  premium. 

Note  that  the  rate  is  for  five  years,  not  for  one  year. 

2.  A  barn  40'  x  100'  x  40',  costing  3^  per  cubic  foot,  is  in- 
sured for  3  yr.  at  a  rate  of  i  1  per  $  100.  What  is  the  insurance 
company's  net  loss  if  the  barn  is  totally  destroyed  by  fire? 

3.  A  house  is  insured  in  three  companies.  One  fourth  the 
insurance  is  carried  by  Company  A,  at  20^  per  $100;  five 
eighths  is  carried  by  Company  B  at  1 J  %  ;  and  the  remainder 
is  carried  by  Company  C  at  1J%.  What  is  the  total  cost  of 
insurance  if  the  insurable  value  of  the  house  is  $10,000? 

4.  A  building  is  insured  for  1  yr.  at  45^  per  flOO, 
insurable  value  $15000.  How  much  of  the  premium  must 
be  returned  by  the  company  if  the  insurance  is  canceled  at 
the  expiration  of  four  months  (1)  by  the  company?  (2)  by 
the  insured?  (The  short  rate  for  4  mo.  is  70%  of  the 
annual  premium.) 


LIFE   INSURANCE  189 

5.  A  house  50'  x  40'  x  40',  costing  10  ^^  per  cubic  foot,  with 
an  addition  14'  x  16'  x  10',  costing  5^  per  cubic  foot,  was 
insured  for  1  yr.  at  50  fi  per  f  100.  At  the  end  of  60  da., 
the  policy  was  canceled  by  the  owner.  What  amount  was 
returned  to  the  insured  ?  (The  short  rate  for  60  da.  is  30  % 
of  the  annual  premium.) 

6.  A  house  valued  at  $10,000  is  insured  in  one  company 
for  13000,  in  another  for  $2000.  A  loss  of  $8000  is  sus- 
tained. Under  a  coinsurance  clause,  how  much  loss  must  be 
borne  by  the  owner? 

7.  A  company  carries  insurance  on  its  stock  of  merchan- 
dise, valued  at  $25,000,  to  the  amount  of  $12,500  under  a 
policy  containing  the  coinsurance  clause.  In  the  event  of  a 
$4850  loss,  what  will  the  company  receive  from  the  insurance 
company  ? 

LIFE   INSURANCE 

311.  In  life  insurance,  the  contingency  insured  against  is 
the  death  of  the  insured.  The  policy  may,  however,  agree 
to  pay  a  fixed  sura  at  the  expiration  of  some  specified  time. 

On  the  death  of  the  insured,  the  amount  of  the  policy  is 
paid  to  some  one  named  in  the  policy,  called  the  beneficiary. 

312.  Life  insurance  policies  may  be  classified  as  whole- 
life,  term,  and  endowment. 

313.  In  whole  life  policies  the  face  of  the  policy  is  payable 
at  the  death  of  the  insured. 

314.  In  term  policies  the  sum  insured  is  payable  only  if 
death  occurs  within  a  stated  period ;  after  this  period  the 
policy  lapses. 

315.  An  endowment  policy  provides  for  the  payment  of  a 
stated  sum  to  the  insured  at  the  expiration  of  a  stated 
period,  if  he  is  then  living ;  or  to  his  beneficiary  in  case 
of  death  before  that  time. 


190  INSURANCE 

316.   liiites  for  ilOOO  insurance. 


Whole-life 

Endowment 

Age 

Ordinary 
Life 

lO-pavinent 
Life 

20-i)avinent 
Life 

10  Years 

15  Years 

20  Years 

21 

•S  10.16 

47.26 

20.22 

103.01 

66.34 

47.73 

22 

10.56 

47.08 

20.66 

103.10 

65.04 

47.83 

23 

10.08 

48.72 

30.13 

103.10 

66.04 

47.94 

2i 

20.42 

40.48 

30.64 

103.29 

66.15 

48.06 

25 

20.88 

60.27 

31.14 

103.39 

66.26 

48.18 

26 

21.36 

61.00 

31.67 

103.49 

66.38 

48.31 

27 

21.87 

51.06 

32.24 

103.60 

66.50 

48.45 

28 

22.41 

52.83 

32.81 

103.73 

66.63 

48.61 

29 

22.08 

53.72 

33.30 

103.86 

66.78 

48.78 

30 

23.68 

54.66 

34.01 

103.00 

66.04 

48.06 

31 

24.21 

66.62 

34.66 

104.13 

67.11 

49.16 

32 

24.88 

66.63 

35.32 

104.20 

67.29 

49.37 

33 

26.50 

57.66 

36.01 

104.46 

67.48 

40.60 

34 

26.34 

58.73 

36.73 

104.64 

67.69 

40.86 

35 

27.13 

50.85 

37.40 

104.84 

67.92 

50.12 

36 

27.00 

61.00 

38.28 

106.06 

68.17 

60.42 

37 

28.86 

62.10 

30.11 

105.28 

68.44 

60.76 

38 

20.70 

63.43 

30.08 

105.63 

68.73 

51.11 

39 

30.78 

64.71 

40.87 

106.80 

69.06 

61.61 

40 

31.83 

66.03 

41.83 

106.09 

69.41 

61.96 

The  above  is  taken  from  the  rate  book  of  one  of  the  large 
companies. 

It  is  advisable  to  secure  sample  policies  for  examination 
of  cash  values,  extended  insurance,  etc. 


EXERCISES 

1.  Find  the  annual  cost  of  an  ordinary  whole-life  policy 
for  ^3000  at  the  age  of  25  yr. 

According  to  the  table  the  rate  per  1 1000  at  age  25  is  $20.88. 
On  13000  the  premium  (cost)  is  3  x  $20.88,  or  $62.64. 


LIFE   INSURANCE  191 

.    2.    What  is  the  annual  cost  of  a  110,000  policy  on  the  life 
of  a  man  30  yr.  of  age  on  the  ordinary  whole-life  plan  ? 

3.  A  man,  age  33,  insures  for  15000  on  the  15-year  endow- 
ment plan.  At  the  expiration  of  the  period,  how  much  more 
than  the  face  of  the  policy  will  he  have  paid  the  company 
in  premiums  ? 

4.  How  much  would  the  payments  in  the  preceding 
problem  amount  to  at  2%   compound  interest? 

5.  A  man  30  yr.  of  age  took  two  policies ;  one  for  $1000 
on  the  20-payment  life  plan,  the  other  for  11000  on  the 
20-year  endowment  plan.  At  the  expiration  of  the  20  yr. 
the  value  of  the  20-payment  life  policy  was  $555 ;  the  value 
of  the  endowment  policy  was  flOOO.  As  an  investment, 
which  was  the  better  policy  if  money  was  worth  3%  per 
year?     (Use  Annuity  table,  page  156.) 

6.  A  merchant  34  yr.  old  took  out  $10,000  of  ordinary  life 
insurance  as  a  means  of  protection  to  his  creditors.  What 
premium  does  he  pay  ? 

7.  A  15-yr.  endowment  policy  for  $2000,  written  on  the 
life  of  a  man  37  yr.  old,  is  deposited  as  collateral  for  a  loan 
of  $-100  at  7  %.  What  is  the  cost  of  premium  and  interest 
annually  ? 

8.  A  man  29  yr.  old  pays  a  premium  of  $207.72  on  a 
10-yr.  endowment  policy,  and  $133.56  on  a  20-payment  life 
policy.      How  much  insurance  does  he  carry  ? 


STOCKS   AND   BONDS 
STOCKS 

317.  Stock  companies  are  associations  of  persons  authorized 
by  law  to  transact  business  as  one  individual.  They  are 
called  incorporated  companies,  or  corporations. 

318.  Stocks  represent  the  capital,  property,  etc.,  which 
a  company  invests  in  a  business  under  the  law  of  the 
state. 

319.  A  share  represents  a  certain  equal  part  of  the  capital 
stock.  Shares  are  of  any  value  assigned  to  them,  as  $25, 
150, 1100. 

320.  A  stock  certificate  is  a  printed  statement,  signed  by 
the  officers  of  an  incorporated  company,  stating  the  number 
of  shares  owned,  the  par  value  of  each,  etc.,  to  which  the 
holder  is  entitled. 

321.  The  par  value  is  the  value  assigned  to  the  stock  by 
the  corporation. 

322.  The  market  value  is  the  value  for  which  stock  can 
be  sold.  It  depends  upon  the  dividends  paid,  security 
of  the  business,  business  conditions,  etc.  The  market  value 
is  the  quoted  value,  and  may  be  par^  above  par,  or  below  par. 
Thus,  par  being  8100,  a  stock  quoted  at  123  is  above  par; 
at  76  it  is  below  par. 

323.  A  dividend  is  a  certain  amount  of  profit,  based  upon 
the  par  value  of  the  stock,  divided  among  stockholders. 

324.  An  assessment  is  a  sum  levied  upon  stockholders  to 
make  up  losses,  to  make  improvements,  etc. 

192 


STOCKS 


193 


325.   Preferred  stock  is  stock  to  which  some  preference  has 
been  given,  over  other  stock  issued  by  a  corporation.     It 


A  Certificate  of  Stock 

receives  the  first  profits  distributed,  sometimes  at  a  guar- 
anteed rate  per  cent. 

Note.  There  are  so  many  different  kinds  of  stock  issued  that  inves- 
tigation of  the  constitution  and  by-laws  of  the  corporation  is  the  only  safe 
guide  for  anyone  investing  in  its  stock. 

326.  Common  stock  is  stock  generally  issued  by  companies, 
and  carries  with  it  no  guarantee  of  dividends. 

327.  A  stockbroker  is  a  person  who  makes  a  business  of 
buying  and  selling  stocks  for  others ;  he  usually  charges,  as 
commission,  or  brokerage,  ^  of  1  %  of  the  par  value  of  the 
stock  on   each  transaction.     In  some  small  exchanges  the 


charge  is  ^  of  1 


will  he  taken  as  the  charge  in  all 


problems  in  this  book  unless  otherwise  stated. 
BUS.  abith.  — 13 


194 


STOCKS  AND  BONDS 


EXERCISES 

1.  A  manufacturing  company  capitalized  at  $  12000  declares 
a  dividend  of  16|  %.  Find  the  dividends  of  a  stockholder 
who  bought  20  shares  of  stock  at  the  par  value  of  $100. 

162%=!. 

20  X  i  100  =  .1^2000,  stockholder's  investment, 
iof  i2000  =  $333J. 

2.  An  investment  of  ^i  112,420  was  made  in  Northern  Pacific 
at  127|.    The  stock  pays  regular  dividends  of  7  %.    Find  the 

'  127 1  +  i  (brokerage)  =  127|,  cost  per  share. 
112,420-1271  =  880  shares, 
f  100  X  880  X  .07  =  16160,  dividends. 
(Dividends  are  always  figured  on  the  par  value.) 

3.  A  man  invests  in  Amalgamated  Copper  at  83,  includ- 
ing brokerage.  If  this  stock  pays  5  %,  what  per  cent  of  in- 
come will  he  get  from  an  investment  of  $1992  ? 

1992  -5-  83  =  24  shares. 
f  100  X  .05  =  $5,  dividend  per  share. 

$5  X  24  =  $120,  income. 
120^-1992  =  6/^%. 

Find  the  investment  in  each  of  the  following,  par  value 
being  $100  and  brokerage  being  |^  of  1  %  on  the  par  value. 


Quantity 

Stock 

Pbicb 

Cost 

Com. 

Total  Cost 

4. 

40 

Ches.  &  Ohio 

69J 

$2770 

$6 

$2776 

00 

5. 

60 

Mo.  K.  &  T. 

271 

6. 

120 

Union  Pac. 

169| 

7. 

74 

Erie  R.  R. 

33| 

8. 

150 

Gen.  Elec. 

160 

9. 

24 

Erie  2  pfd. 

42 

10. 

200 

U.  S.  Steel 

70 

11. 

31 

Nat'l  Bis. 

130 

12. 

8 

Amal.  Copper 

78J 

13. 

65 

Am.  C.  &  F. 

54 

STOCKS 


195 


14.  A  stock  of  par  value  of  $25  pays  a  yearly  dividend  of 
$4.28  per  share.  What  is  the  rate  of  income  from  this 
stock  ? 

15.  What  can  I  afford  to  pay  for  a  stock  paying  annual 
dividends  of  §7.35  per  share  in  order  to  net  5|  %  on  the 
investment?     (No  brokerage.) 

Fill  in  the  necessary  amounts  in  the  following : 


Quantity 

Stock 

Price 

Cost 

Com. 

Total  Cost 

16. 

50 

Amer.  Can 

4U 



_ 

_ 

17. 

— 

Diamond  Match 

107 

15350 

— 

— 

18. 

— 

People's  Gas 

1171 

— 

$2.50 

— 

19. 

100 

Kan.  C.  &  S. 

— 

— 

— 

82637 

50 

20. 

— 

111.  Cent. 

128f 

1543 

50 

— 

— 

21. 

— 

N.  &  W. 

— 

3227 

3.60 

— 

22. 

35 

C.  M.  &  St.  P. 

— 

— 

— 

3731 

88 

23. 

— 

West.  Union 

— 

— 

12.50 

6137 

50 

24. 

— 

Quaker  Oats 

375 

— 

— 

45015 

25. 

— 

D.  L.  &  W. 

— 

6932 

— 

6934 

26.  Find  the  income  on  *n  investment  of  1^4340  in  Balti- 
more &  Ohio  R.  R.  at  108|,  brokerage  |^,  if  the  stock  pays 
5%  dividends. 

27.  If  the  money  in  problem  4  was  borrowed  through  a 
bank  at  6  %,  what  was  the  income  ? 

28.  A  man  buys  50  shares  of  Union  Pacific  common  at 
172|^,  and  sells  them  at  175|.  If  the  broker  charges  ^%  on 
all  transactions  through  his  office,  what  was  the  man's  gain  ? 

29.  If  P.,  C,  C,  &  St.  L.  pays  7%  dividends,  what  in- 
vestment, through  a  broker,  at  109|,  brokerage  |  %,  will  pay 
an  annual  income  of  f  2350  ? 

30.  A  broker  owns  300  shares  of  National  Biscuit  Co. 
stock  which  pays  8%  annual  dividends.     He  sells  at  137|- 


196 


STOCKS  AND  BONDS 


and  invests  the  proceeds  in  U.  S.  Steel  pfd.,  paying  t)|  %, 
at  111|.  Is  his  income  increased  or  diminished  and  how 
much  ?     (No  brokerage.) 

31.  Find  the  cost,  inchiding  brokerage,  of  450  shares  of 
stock  paying  5%  dividends  on  a  par  value  of  {^100  per  share, 
if  the  income  from  the  investment  is  4%. 

32.  An  investor  can  buy  Pullman  Co.  stock  paying  12%, 
at  ItjOJ,  or  Pittsburgh  Coal  pfd.  paying  8%,  at  90|.  He 
chooses  500  shares  of  the  former  stock.  Is  his  income  more 
or  less,  and  how  much,  than  it  would  be  on  500  shares  of 
Pittsburgh  Coal,  brokerage  ^  %  on  each  transaction  ? 


BONDS 

328.  A  bond  is  an  obligation  to  pay  a  certain  sum  of 
money  at  a  stated  time,  with  a  fixed  rate  of  interest  payable 
at  regular  intervals.  Interest  payments  are  usually  made 
on  Jan.  1  and  July  1. 

Bonds  are  named  for  the  government,  corporation,  city, 
etc.,  issuing  them ;  for  the  time  they  are  run,  as  lO-yr., 
20-yr.,  etc. ;  for  the  security  they  offer,  as  first-mortgage, 
extension,  refunding,  etc. 

Spanish  War  3's  were  bonds  issued  by  the  govern- 
ment during  the  Spanish  War,  bearing  3%  interest.  Other 
titles,  indicating  the  kind  of  bond,  are :   Panama  Canal  2's, 

Cleveland  City  4's, 
Denver  Gas  5's, 
Valley  Traction 
5's,  etc. 

329.    A    coupon 

bond  is  a  bond  hav- 
ing certificates  or 
Coupon  from  a  CotftoN  Bond       ^  coupons    attached, 


THE  OHIO  GRAVEL  AND  SANO  COMPANY. 


No.. 


December  1,1912. 


The  Ohio  Gravel  and  Sand  Company,  on  the  first  day  of  Decem- 
ber. 1917.  will  pay  to  bearer  seventeen  dollars  and  fifty  cents, 
($17.50),  in  Gold  coin  of  the  United  States,  of  the  standard 
existintr  July  1,  1901.  at  the  office  of  The  Citizens  Trust  and 
Savings  Uank.  Columbus.  Ohio,  being  six  months  interest 
then  due  on  its  seven  (7)  per  centum  first  mortcage  bond, 
all  terms  and  conditions  of  which  are  made  part  hereof. 


'r  Oin!^  Sn. 


For  value  received,  The  Ohio  Gr,  . ■ :  ;- !  ,~  :  i  '  r:ipany,  a  coiporation  duly  oroanized  under  the  laws  of  the 
ISP  this  bond  shall  be  registered  as  hereinafter  provided,  then 
registered  owner  hereof,' on  or  before  the  I  si  day  of  December.  1917,  Five  Hundred  ($500.00)  Dollars  in 
Gold  coin  of  the  United  Sutes,  of  the  present  standard  of  weight  and  fineness,  with  interest  thereon  in  like  gold 
coin,  from  the  first  day  of  December,  1 9 1 2,  at  the  rate  of  seven  (7)  per  centum  per  annum,  payable  semi-annually, 
on  the  I  St  day  of  June  and  December,  of  each  year,  to  the  bearer  of  the  annexed  coupons. 

The  principal  and  interest  of  this  bond  are  payable  at  the  office  of  The  Citizens  Trust  and  Savings  Banlc, 

ender  of  this  bond  and  the  annexed  coupons  as  they  severally  mature.     This  bond  is 

ate  and  amount,  numbered  consecutively  from  one  ( 1 )  to  fifty  (50), 


Columbus,  Ohio,  upon  ttie 

one  of  a  ^lies  of  finy  (50)  bonds,  all  of  like  tenor 

both  inclusive,  all  of  which,  wjth  interest  coupons  attached,  without  preference 

distinction  between  principal  and  interest,  are  secured  by  a  certain  first  morlgagi 

ized,  executed  and  delivered  by  The  Ohio  Gravel  and  Sand  Company  to  Lowry  F.  Sater,  as  Trustee, 

to  said  Lowry  F.  Saler,  certain  lands  and  properties  therein  referred  to  and  described,  in  trust, 

ment  of  all  said  bonds  and  ' 


ir  pnority  among  them,  and  witiK>u( 
first  mortgage  of  even  date  herewith,  duly  audior- 


novided  in  said  mortgage  deed,  and  subject  ( 
lumbers,  commencing  with  the  lowest  numb< 
1  or  before  the  first  day  of  December,  1917. 


:  the  p»y- 
I  interest  aforesaid. 

Said  bonds  are  entitled  to  the  benefit  of  a  tinkmg  hmd 
redemption  either  from  the  sinking  fund  or  otherwis< 
outstanding,  at  any  interest  bearing  period.  < 

All  redemptions  prior  to  December  I,  1917,  at  the  rates  and  premiums  aforesaid,  shall  be  optional  with  said 
promisor  and  shall  be  made  only  upon  its  written  direction  given  and  delivered  to  the  trustee  at  least  two  (2)  months 
before  the  date  of  the  redemption  next  following  such  notice,  and  thereafter,  the  sinking  hmd  shall  be  applied  by 
the  trustee  to  the  redemption  of  bonds  at  their  face  value  and  accrued  interest  without  such  written  direction. 

If  any  default  shall  be  made  in  any  of  the  payments  of  interest  on  tliis  bond,  or  in  the  payments  into  the  sink- 
ing fund  as  provided  in  said  mortgage;,pr  in  the  pa)in<*iJ  of  any  taxes  pi"  assessments  lawfully  made  or  levied  upon 
the  whole  or  any  part  of  the  property  itude  ietUrity  lie?«for,  md  if  any  such  default  «hall  continue  for  a  period  of 
six  (6)  months  after  written  notice  thereof  to  i»i(ia  xofclfe^jhy  said  trostee.  or  by  the  holder  of  this  bond,  or  of 
any  of  its  interest  coupons  thenduer  and  .iln6iy,f(b«B(i4ff  in,  ahy'siicheveBt,'  at  the'option  of  the  holder  hereof, 
this  bond  and  accriied  interest  ,fha1l  theVeupoi  .ftcoipK  (iJiV.  ^  t)ayablc. 

This  bond  may  be  registered  in  the  owrtef  s  name  oji  ^ihe  boob  of  'siid  Tile  Ohio  Gravel  and  Sand  Company, 
at  the  Hartman  Building,  in  the"  City  of  Columbus,  Ohio,  such.regirtry  to  be  Bofcd  oh  the  bond  by  the  company's 
registration  agent,  after  which  no  transfer  will  \x  valid  'ufl«*  made  on  the  books  of  Said  company  by  the  registered 
owner  or  his  attorney,  and  similarly  noted  on  this  bond,  but  the  same  may  be  discharged  from  registry  by  being 
duly  transferred  to  bearer,  afler  which  it  shall  be  transferable  by  delivery,  and  it  shall  continue  subject  to  successive 
registrations  and  transfers  to  bearer  as  aforesaid,  at  the  option  of  each  holder.  Such  registry  of  this  bond  shall  not 
restrain  or  affect  the  negotiability  of  the  attached  interest  coupons  by  delivery  merely,  but  unredeemed  conpons  may 
be  surrendered  at  any  tim*.  and  the  insullments  of  interest  made  payable  thereafter  Only  to  the  registered  owner  of 
tliis  bond,  such  surrender  to  be  noted  on  the  bond  by  the  company's  registration  agent  This  bond  shall  be  con- 
tidoed  iuued  oiOy  when  the  trustee's  certificate  hereon  is  duly  executed  by  Lowry  F.  Sater.  as  Tjrustee. 

3n:  SliltltBiI  9)l^irtof,  the  said  The  Ohio  Gravel  and  Sand  Company  hat  tamed  these  - 
pieaents  to  be  signed  by  its  President  and  its  corporate  seal  to  be  annexed,  attested  by 
its  Secretary,  and  tlie  attached  coupons  to  be  aulhenbcated  by  the  fac  simile  of  the 
:  of  its  Secretary  engraved  tWeoti.  this  1st  day  of  December.  1912. 
THE  OHIO  GRAVEL  &  SAND  COMPANY, 


198 


STOCKS  AND  BONDS 


showing  the  amount  of  interest,  when  due,  and  where  pay- 
able. There  is  one  coupon  for  each  interest  payment,  to  be 
detached  and  negotiated  like  any  other  commercial  paper. 

330.  A  registered  bond  is  a  bond  payable  to  the  owner 
whose  name  is  registered  in  the  books  of  the  issuing  company. 
A  registered  bond  can  be  transferred  only  by  assignment. 

331.  The  value  of  a  bond  depends  on  the  security  back 
of  it,  on  the  rate  of  interest  it  pays,  and  on  the  time 
it  has  to  run.  Values  are  affected  by  current  money  rates 
just  as  any  other  values  are  affected  by  them. 

The  ^  usual  par  value, 
called  denomination^  of  a 
bond  is  $1000.  No  frac- 
tional part  of  a  bond  can 
be  purchased. 

The  following  table, 
called  a  bond  table,  is  used 
in  determining  the  value 
of  a  bond,  which  has  20 
yr.   to  run. 

'J'he  left-hand  column  gives 
the  rate  of  income ;  the  top  row 
gives  the  rate  paid  on  the  bond ; 
the  figures  in  the  body  of  the 
table  show  what  can  be  paid  for 
any  given  bond  to  net  a  certain 
per  cent  on  the  investment. 
Thus,  a  5%  bond,  if  bought  for 
Ilia  68,  will  net  4%  ;  if  bought 
at  f  110.04,  will  net  4^%,  etc. 

Likewise,  a  3%  bond,  bought 
at  184.78  will  net  4^%. 

Also,  a  man  wishing  to  make 
an  investment  on  a  .5J  %  basis 
might  buy  a  4^  %  bond  at  $87.96. 


20  YEARS— Interest  Payable  Senrf-^nnaally.  | 

Itetper 

IB- 

Bom. 

BONDS  BBARINO  INTEREST  AT  THE  RATE  OP  | 

7% 

6% 

6% 

4i% 

4% 

3^% 

3% 

4 

141.03 

127.36 

113.68 

106.84 

100.00 

93.16 

86.32 

4.10 

4.20 

139-32 
138.90 

137-63 

125.76 
126.37 
124.19 

112.20 
111.84 
110.75 

105.42 
106.07 
104.03 

98.64 

98.31 
97-3J 

91.86 
91.64 

90.59 

85.09 
84.78 

8387 

4X 

136.80 

123.42 

110.04 

lOS.M 

96.65 

89.96 

83.27 

4.30 

4.40 

'35-98 
134,76 

134.35 

122.65 
121.61 
121. 14 

109-33 
108.27 
107.93 

102.66 
101.66 

101.32 

96.00 
95.04 
94.72 

88.11 

82. 68 
81.80 
8..51 

*>i 

132.74 

119.65 

106.65 

100.00 

93.45 

86.90 

80.35 

4.60 

4.70 

131-16 
130.77 
r29.6i 

118. 18 
117.82 
116.74 

105.19 
104.86 
103.86 

98.70 

98.38 
97-43 

92.21 
91.90 
90.99 

85-72 
85.42 
84.55 

79.22 
78.94 
78.1. 

43< 

128.84 

116.02 

103.20 

96.80 

90.39 

83,98 

77.67 

4.80 

490 

128.08 
126.95 
126.58 

115-32 
114.27 
113-92 

102.55 
101.69 
101.27 

96.17 
96.24 

94-94 

89.79 
88.90 
88. 61 

83.40 
82,66 

82.28 

•77-02 
76.22 

75 '95 

6 

125.10 

112.66 

100.00 

93.72 

87.45 

81.17 

74.90 

5.10 

5.20 

123-65 
123.29 
122.22 

111.20 
110.87 
109.87 

98.76 

98.45 

97-53 

92-53 
92.24 
91-36 

86. 31 
86.03 

85-19 

80.09 
79".  82 
79-02 

73.86 
73.61 

72.85 

y/ 

121.51 

109.22 

96.93 

90.78 

84.64 

78.49 

72.34 

5.30 
5.40 

120.81 
119.77 
119.42 

108.57 
107.60 

107.28 

96.33 
95.44 

95-14 

90.21 
89.86 

89.07 

84.09 
83.27 

83.01 

77-97 
77.19 

76.94 

71-85 
71.11 

70.87 

y/i 

118.06 

106.02 

93.98 

87.96 

81.94 

75.92 

69.90 

116.38 
114.74 
"3.13 

104.47 
102.95 
101.46 

92.55 
91.16 
89.78 

86.59 
85.26 
83-95 

80.64 
79.36 
78.11 

74. 6S 
73.46 
72.27 

68. 72 
67.67 
66.43 

6 

111.56 

100.00 

88.44 

82.66 

76.89 

71.11 

65.33 

6'A 
6^- 

108.50 
105.65 
102.72 

97-17 

94.45 
91-83 

85.84 
83.34 
80.95 

80.18 
77.79 
75-50 

74-51 
72.24 
70.06 

68.85 
66.69 
64.62 

63-19 
61.14 

59-17 

7 

100.00 

89.32 

78.64 

73.31 

67.97 

62.63 

67.26 

BONDS  199 

EXERCISES 

Allow  for  no  brokerage  in  the  first  seven  problems. 

1.  Using  the  table,  find  the  price  at  which  20-yr.  bonds 
can  be  bought  to  yield  as  follows  : 

5%  bond  to  yield  41%. 
6%  bond  to  yield  5.4%. 
4i%  bond  to  yield  5.3%. 

2.  Find  the  rate  of  income  on  20-yr.  bonds  bought  as 
follows : 

6%  bonds  bought  at  114.27. 
3|  %  bonds  bought  at  par. 
5%  bonds  bought  at  80.95. 

3.  A  man  invested  in  first-mortgage  industrial  bonds  bear- 
ing 5  %  at  a  price  which  yielded  him  4.80  %.  What  was  the 
quoted  price  ? 

(In  this  problem,  and  in  those  to  follow,  consider  all  bonds 
as  maturing  in  20  yr.  ;  interest  coupons  as  due  Jan.  1  and 
July  1.) 

4.  An  issue  of  $15000  of  5%  bonds  is  sold  for  f  14,449.50. 
What  rate  do  they  pay  the  purchaser  ? 

5.  On  June  12,  I  purchased  five  1 1000  3J%  bonds  quoted 
at  82  and  interest.     How  much  do  I  pay  for  them  ? 

Suggestion.  Compute  the  accrued  interest  from  the  time  of  the  last 
payment,  and  add  to  the  quoted  price. 

6.  If  I  buy  a  $1000  7%  bond  at  102.8  +  127.50  accrued 
interest,  what  is  the  rate  of  income  on  my  investment  ? 

7.  A  Paris,  France,  municipal  loan  of  141,000,000  3% 
bonds  was  oversubscribed  70  times,  that  is,  the  subscription 
amounted  to  12,870,000,000.  If  the  bonds  were  allotted 
pro  rata  according  to  subscriptions,  what  amount  was  awarded 
to  the  man  who  subscribed  for  1130,000  worth? 


200 


STOCKS  AND  BONDS 


8.  A  man  having  17000  to  invest  wishes  to  secure  an 
income  of  4|  %  on  a  4^%  bond.  How  many  81000  bonds 
can  he  buy,  and  how  much  will  he  have  left  of  his  $7000  ? 

Note.  The  broker's  charge  for  the  purchase  or  sale  of  a  bond  is  the 
same  as  for  stocks ;  viz.,  ^  of  1  %,  or  $  1.25  for  each  $  1000  bond. 

Fill  in  the  blank  spaces  in  the  following.  Notice  that 
under  "  quantity  "  the  par  value  of  the  purchase  is  given  in- 
stead of  the  number  of  bonds. 


Quantity 

Bond 

Priob 

Cost 

Com. 

Total  Cost 

9. 

$6000 

C.  &  0.  41'8 

99J 





__ 

10. 

9000 

Cin.  Sewer  4's 

— 

S9225 





11. 

— 

U.  S.  Reg.  2'8  1930 

— 

— 

.$15 

a  12195 

12. 

6000 

Scioto  Val.  5's 

— 

41K)0 

— 

— 

13. 

— 

U.  S.  Mex.  4'8 

— 

8987 

60 

— 

9000 

14.  A  man  deposits  $25000  with  his  broker  for  the  pur- 
chase of  Northern  Pacific  4's  at  98|,  brokerage  |  %.  How 
many  bonds  will  be  purchased  for  him,  and  what  cash  balance 
will  he  have  left  with  the  broker  ? 

15.  Cole  &  Co.,  brokers,  sent  this  statement  to  R.  T.  Allen: 
"  We  have  this  day  bought  for  your  account  and  risk  as 

per  instructions  and  in  accordance  with  the  rules  and  customs 
of  the  New  York  Stock  Exchange,  through  Wilson  &  Co. : 


Quantity 

Stock  or  Bond 

Prick 

Cost 

Com. 

Tax 

Total  Cost 

$4000 
$6600 

A.  E.  &  C.  5'8 
Am.  G.  &  E.  5's 

101 1 
10:} 

— 

— 

— 

?i 

What  is  the  amount  of  R.  T.  Allen's  investment  ?  What 
commissions  do  Cole  &  Co.  get  ?  What  is  the  rate  of  income 
on  the  entire  investment  ? 

Note.  The  tax,  called  a  transfer  tax,  is  a  charge,  paid  by  the  seller, 
on  all  stock  sales.  This  charge  is  2j^  per  share  of  $100  par  value;  the 
tax  on  shares  of  $25  par  value  would  be  50^  per  100  shares. 


EXCHANGE 

332.  Exchange  is  the  term  applied  to  the  transfer  of 
money  from  one  place  to  another  otherwise  than  by  actually 
sending  the  money  itself. 

333.  Exchange  is  domestic,  if  between  two  places  in  one 
country  ;  foreign,  if  between  two  places  in  different  countries. 

334.  There  are  three  important  factors  in  exchange  : 

1.  The  amount  to  be  transferred. 

2.  The  charge  for  such  transfer. 

3.  The  value  of  ready  money  in  one  place  as  compared 
with  that  in  another. 

335.  It  is  not  surprising  that  money  may  have  different 
values  in  different  places.  This  value  depends  on  the  rate 
at  which  it  can  be  borrowed  from  the  banks.  If  the  banks 
in  one  community  have  plenty  of  money  on  hand,  and  there 
is  no  great  demand  for  it,  money  will  be  "  cheap  "  ;  i.e.,  the 
rate  of  interest  on  loans  will  be  low.  But  if  there  is  no 
great  surplus  of  cash  on  hand,  and  much  money  is  needed 
for  carrying  on  business,  money  will  be  "  dear  "  or  "  tight "  ; 
i.e.,  the  rate  will  be  higher. 

336.  The  value  of  money  in  one  place  as  compared  with 
its  value  in  another  is  called  the  rate  of  exchange  between 
these  t'wo  places. 

337.  Rates  of  exchange  fluctuate,  being  governed  by 
trade,  or  business  conditions.  Published  rates  of  exchange 
usually  include  the  cost  of  the  transfer. 

201  * 


202 


EXCHANGE 


338.  The  principal  money  centers  in  the  United  States  are 
New  York,  Chicago,  and  San  Francisco,  and  rates  of  exchange 
are  usually  quoted  as  "  New  York  exchange,"  etc.  Foreign 
exchange  would  be  quoted  as  "  London  exchange,"  "  Paris 
exchange,"  etc. 

DOMESTIC  EXCHANGE 

339.  Money  may  be  transferred  by  : 

(a)  Postal  money  order.  The  government,  through  its 
post  offices,  accepts  money  and  issues  an  order  therefor,  pay- 
able at  any  office  the  purchaser  may  desire.  Postal  money 
orders  are  issued  for  any  amount  up  to  ilOO. 

The  cost  of  transfer  by  postal  money  order,  called  a  "  fee," 
is  determined  by  the  following  table : 

Table 


For  orders  for  sums  not  exceeding   ^2..')0 
If  over    $2.50  and  not  exceeding      $5.00 
If  over    $5.00  and  not  exceeding    $10.00 
If  over  $10.00  and  not  exceeding    $20.00 
If  over  $20.00  and  not  exceeding    $30.00 
If  over  $30.00  and  not  exceeding    $40.00 
If  over  $40.00  and  not  exceeding    $50.00 
If  over  $50.00  and  not  exceeding    $60.00 
If  over  $60.00  and  not  exceeding    $75.00 
If  over  $75.00  and  not  exceeding  $100.00 

3  cents. 

5  cents. 

8  cents. 
10  cents. 
12  cents. 
15  cents. 
18  cents. 
20  cents. 
25  cents. 
30  cents. 

(h)  Express  money  order.  This  is  similar  to  a  postal 
order  except  that  it  is  issued  by  an  express  company  instead 
of  by  the  government. 

The  fee  for  an  express  money  order  is  the  same  as  for  a 
postal  money  order. 

(c)  Telegraphic  money  order.  Telegraph  companies  will 
accept  money  at  au}^  office  and  pay  it  out  at  an}^  other  office 
after  an  exchange  of  telegraphic  messages. 


DOMESTIC  EXCHANGE  203 

The  cost  of  such  transfer  is  greater  than  that  of  other  forms 
of  exchange.  The  sender  must  pay  for  the  sending  of  two 
ten-word  messages,  and  1  %  of  the  amount  transferred.  There 
is  no  charge  less  than  25)^  plus  twice  the  ten-word  rate,  but 
on  amounts  over  #1000,  only  |  %  is  charged  for  the  excess. 

((^)  Bank  check.     (See  §  253.) 

In  local  transactions  involving  bank  checks  there  is  no 
charge  for  collecting. 

Collection  is  usually  charged  on  bank  checks  sent  to  any 
place  outside  the  city  in  which  they  are  issued  or  outside 
the  banking  zone  where  they  are  received.  The  charges 
vary  according  to  the  amount  of  the  check,  the  bank's  ar- 
rangement with  the  customer,  the  distance  between  the  two 
towns,  etc. 

(e)  A  certified  check  is  a  check  across  the  face  of  which 
some  officer  of  the  bank,  usually  the  cashier  or  paying  teller, 
has  stamped  and  signed  a  statement  certifying  that  the  check 
is  good. 


CO  M  a 


A^iKRid^  Trust  &  Savings  Bankl^  '■- 


Dollars 


^^^rL^    /t^h^^^^yL^,^*^  TKptLi^ 


A  Certified  Check 

(/)  Certificates  of  deposit  (see  §  252)  are  issued  without 
charge,  but  are  subject  to  the  usual  rates  of  exchange  if 
cashed  at  a  point  other  than  that  at  which  they  are  issued. 

(^)  A  bank  draft  is  a  check  drawn  by  one  bank  on 
another.  It  is  the  most  common  form  of  exchange  be- 
cause it  is  safe. 


204 


EXCHANGE 


"TUEFjI^TjpTlqjV/JL^/fJVK      ^^ 


Yvncennes.  Ind  °l 


SEC  261912 


153 

502187 


To  THE  NATIONAL  PARK  BANK. 
NE-W  YORK 

1-54 


NOT  OVER  T£M  DOLLAHS  SiOi 

'AC 


A  Baitk  Draft 

Under  some  circumstances  the  cashier  of  the  bank  will 
issue  a  cashier's  check,  instead  of  a  draft.  This  is  merely 
the  bank's  check  drawn  on  itself ;  its  function  is  essentially 
that  of  a  bank  draft. 

(A)  Travelers'  checks  are  issued  by  some  express  com- 
panies as  a  convenience  to  travelers.  They  are  issued  in 
denominations  of  #10,  #20,  $50,  $100,  and  $200.  They 
differ  from  the  money  orders  issued  b}^  these  companies  in 
that  they  are  payable  at  any  office  of  the  company  instead 
of  at  some  designated  office.  The  holder  is  identified  by 
his  signature.  Travelers'  checks  are  also  issued  by  many 
banks  belonging  to  the  American  Bankers'  Association; 
they  are  ca-lled  A.  B.  A.  checks. 


?/^ 


A  Trayelehs'  Check 


DOMESTIC   EXCHANGE  205 

Travelers'  checks  are  issued  at  a  cost  of  |  %  of  the  amount 
with  a  minimum  charge  of  50  j^. 

(^)  A  commercial  draft  is  a  form  of  commercial  paper 
used  commonly  in  collecting  accounts.  It  is  an  order, 
signed  by  the  creditor  or  drawer,  directing  the  debtor,  or 
drawee,  to  pay  a  stipulated  amount  to  a  designated  third 
party,  usually  a  bank. 

For  example :  A  and  B  live  in  different  cities,  and  A 
owes  B  flOO.  B  may  "draw"  on  A  for  the  amount,  using 
a  commercial  draft  for  the  purpose.  B  deposits  this  draft 
with  his  bank,  which  forwards  it  to  a  bank  in  the  town 
where  A  does  business.  This  bank  presents  the  draft  to  A, 
and  if  it  is  honored  (paid)  by  A,  deducts  its  charge  for  col- 
lecting and  remits  the  proceeds  to  B's  bank.  B's  bank 
thereupon  pays,  or  credits,  the  amount  to  B  less  its  charge, 
if  any,  and  the  transaction  is  closed. 


tsi^ 


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A  Commercial,  Draft 

The  charge  for  collecting  commercial  drafts  is  not  fixed 
by  any  rule,  but  is  slightly  larger  than  that  on  other  kinds 
of  exchange  owing  to  the  trouble  of  presenting  and  col- 
lecting. 

Commercial  drafts  usually  read  "  with  exchange "  or 
"without  exchange.'-'  "With  exchange"  means  tliat  the 
collection   charge  is   to  be  added   to  the  face  of  the  draft 


206  EXCHANGE 

when  presented,  and  paid  by  the  person  drawn  on ;  "  with- 
out exchange"  demands  payment  of  only  the  face  of  the 
draft,  and  the  charge  is  deducted  after  collection  and  the 
proceeds  paid  or  credited  to  the  maker  of  the  draft. 

340.  When  a  draft  is  presented  for  payment,  the  person 
on  whom  it  is  drawn  may,  if  he  wishes,  "  accept "  it,  that  is, 
write  across  the  face  of  the  draft  the  word  "  accepted,"  with 
the  date,  and  sign  his  name.  This  acceptance  acknowledges 
the  indebtedness  and  the  correctness  of  the  amount,  and  vir- 
tually constitutes  a  promise  to  pay.  The  accepted  draft  is 
held  until  due,  and  then  presented  for  payment. 

341.  A  protest  is  a  written  or  printed  declaration  by  a 
notary  public  that  a  negotiable  paper  has  been  dishonored ; 
i.e.^  payment  has  been  refused. 

342.  A  sight  draft  is  a  commercial  draft  calling  for  pay- 
ment "  at  sight "  or  at  presentation. 

343.  A  time  draft  is  a  commercial  draft  calling  for  pay- 
ment at  some  future  time,  say  in  3  da.,  10  da.,  30  da.,  etc. 

344.  The  person  drawn  on  may  honor  a  commercial  draft 
in  two  ways :  by  immediate  payment,  or  by  acceptance. 
(See  §  340.) 

345.  Charges  for  exchange  ought  never  to  exceed  the 
cost  of  shipping  the  actual  money.  In  general  they  may 
be  divided  into  two  classes  : 

1.  Those  paid  by  the  sender  by  the  purchase  of  an  order, 
payable  at  par  at  the  point  to  which  the  money  is  sent. 
These  include  bank  drafts,  money  orders,  etc. 

2.  Thosie  paid  by  the  recipient  of  the  money  on  the  re- 
ceipt of  an  order  payable  at  the  point  from  which  the  money 
is  sent.  These  include  bank  checks,  commercial  drafts 
without  exchange,  etc.  ^ 


DOMESTIC  EXCHANGE  207 

346.  New  York,  Chicago,  and  San  Francisco  being  the 
principal  money  centers  of  the  United  States,  most  ex- 
change is  drawn  against  banks  in  those  cities.  Any  large 
city,  however,  is  a  money  center  for  the  territory  surround- 
ing it,  and  banks  in  small  towns  issue  drafts  on  banks  in 
these  various  centers. 

347.  The  rate  of  exchange  (§  336)  is  usually  quoted  in 
cents  per  $1000  premium  or  discount.     Thus: 

At  Detroit New  York  exchange  at  par. 

At  Louisville New  York  exchange  at  20  f^  premium. 

At  St.  Paul  .     .     .     .     .     .     .  New  York  exchange  at  45^  premium. 

At  Denver New  York  exchange  at  80^  premium. 

At  Chicago New  York  exchange  at  15  ^  discount. 

EXERCISES 

1.  What  is  the  cost  of  a  postal  or  express  money  order  for 
11.12?   for  $23.70?   for|75?   for  15.95?   for  117.25? 

2.  The  ten-word  telegraphic  rate  from  Cincinnati  to 
Dallas  being  60  j^,  how  much  will  it  cost  to  send  ilOO  by 
telegraphic  money  order  ? 

3.  A,  in  Boston,  sends  to  B,  in  Denver,  his  personal  check 
for  12.50.  The  charge  for  collection  is  Jg  %.  How  much 
does  B  receive  on  the  check  ? 

4.  What  is  the  cost  of  sending  $328.50  by  express  money 
order?   $125?   $157.50?   $418.33? 

Suggestion.  Distinguish  between  the  cost  of  the  order  which  includes 
the  amount  sent  and  the  cost  of  sending. 

5.  A,  in  Cincinnati,  wishes  to  send  B,  in  Minneapolis, 
$2456.87.  If  the  collection  charge  is  ^^  %,  for  how  much 
must  A  draw  his  check  to  cover  the  amount  plus  the  charge? 

6.  If  New  York  exchange  is  quoted  at  70  ^  premium, 
how  much  will  the  following  New  York  drafts  cost  :  $850, 
$ 2378.60,  $1200,  $10000,  $375  ? 


208  EXCHANGE 

7.  A  bank  charges  5^  for  each  draft  on  Chicago  of  i25 
or  less,  10  ^  on  125  to  i50,  and  15  i  on  150  to  *100.  How 
much  will  each  of  the  following  drafts  cost:  $7.55,  $23.61, 
i87.19,  $66.90,  140?  What  check  will  cover  the  cost  of 
all  the  drafts  ? 

8.  An  Indianapolis  merchant  owes  a  New  York  importer 
$890.25.  There  is  an  agreement  between  them  that  payment 
is  to  be  made  in  New  York  exchange,  but  that  the  importer 
is  to  pay  the  charge.  If  New  York  exchange  is  quoted  at  |  % 
premium  in  Indianapolis,  for  what  amount  must  the  draft  be 
made  ? 

9.  A  certificate  of  deposit  for  #  500,  issued  by  the  City 
National  Bank  of  Columbus,  Ohio,  Jan.  15,  1914,  draws  3  % 
interest.  It  is  cashed  in  Milwaukee  on  Nov.  15,  1914,  the 
collection  charge  being  -^^  %.  How  much  is  paid  for  it  by 
the  Milwaukee  bank  ? 

10.  How  much  will  a  person  pay  for  10  travelers'  checks 
of  $20  each  ?   for  10  of  $  100  each  ? 

11.  If  San  Francisco  exchange  is  quoted  at  -^-^  %  discount, 
what  will  be  the  cost  of  drafts  on  a  San  Francisco  bank  for 
$1800,  $5000,  and  $1250? 

12.  On  July  16,  A  drew  on  B  for  $450  at  30  da.  sight, 
without  exchange,  and  placed  the  draft  with  his  bank  for 
collection.  Allowing  four  days'  time  in  the  mails,  on  what 
date  may  A  expect  returns  from  the  draft,  and  what  will  be 
the  proceeds,  if  the  collection  charge  is  J  %? 

13.  A  Cleveland  manufacturer  sells  goods  to  a  dealer  in 
Decatur,  111.,  on  Nov.  1,  amounting  to  $2750.60,  net  30  da. 
By  agreement  the  manufacturer  draws  on  the  dealer  on  Dec. 
1  at  sight,  with  exchange.  For  what  amount  must  the  dealer 
draw  his  check  to  meet  the  draft,  if  the  exchange  (charge) 


FOREIGN  EXCHANGE 


209 


14.  Smith  &  Co.,  of  St.  Louis,  sell  Jones  &  Co.,  of  Grand 
Rapids,  Mich.,  goods  amounting  to  11976.50,  f.  o.  b.  cars 
St.  Louis.  Smith  &  Co.  draw  on  Jones  &  Co.  at  sight,  less 
2  %  for  cash.  The  bank's  charge  for  handling  the  draft  is 
^  %,  to  be  paid  by  Jones  &  Co.  How  much  will  Jones  &  Co. 
liave  to  pay  in  order  to  get  the  goods  from  the  railroad  com- 
pany, the  freight  charges  being  $  72.41  ? 

348.  The  clearing  house  is  an  organization  of  banks  in  a 
large  city  for  the  purpose  of  exchanging  local  checks. 

1.  Determine  the  balance  for  or  against  each  bank  in 
the  following  clearing  house  statement.     Check  your  work. 


Bank  No. 

Ck. 

Dr. 

('R. 

Dk. 

1 

1 123678 

04 

$  125919 

21 

2 

87664 

13 

82479 

20 

3 

108362 

87 

101475 

78 

4 

52117 

69 

63540 

03 

5 

72604 

10 

71012 

61 

FOREIGN  EXCHANGE 

349.  When  money  is  sent  from  one  country  to  another, 
the  sending  agent  (post  office,  express  company,  or  bank) 
converts  the  amount  to  be  sent  into  terms  of  the  money  of 
the  country  to  which  it  goes. 

350.  Money  is  thus  transferred  by  :  (a)  postal  money 
orders,  (6)  express  money  orders,  (c)  telegraphic  or  cable 
money  orders,  (c?)  travelers'  checks,  (e)  letters  of  credit, 
(/)  bills  of  exchange. 

351.  On  money  orders  and  travelers'  checks,  and  on 
letters  of  cre4it,  the  cost  of  exchange  is  determined  by  pub- 

BUS.    ARITH,  —  14 


210  EXCHANGE 

lished  rates.  On  bills  of  exchange  it  varies  according  to 
the  money  market,  as  determined  by  conditions  of  trade. 

I  %  is  usually  charged  for  issuing  travelers'  checks. 

The  charge  for  cable  transfer  is  the  cable  rate  of  exchange, 
plus  \  %  commission,  plus  the  telegraph  and  cable  charges. 

352.  Letters  of  credit  are  issued  by  bankers.  They  call 
for  the  payment  of  a  specified  amount  at  any  one  of  a  num- 
ber of  banking  institutions  in  various  parts  of  the  world. 

The  usual  charge  for  issuing  a  letter  of  credit  is  1  %. 

353.  Bills  of  exchange  include  bank  and  commercial 'drafts, 
checks,  etc.,  used  in  the  transfer  of  funds  from  one  country 
to  another.     They  include  : 

(a)  Those  issued  by  banks.  These  are  used  in  foreign 
exchange  just  as  bank  drafts  are  used  in  domestic  exchange. 
They  are  sometimes  issued  in  duplicate  or  triplicate,  the 
various  copies  being  sent  by  different  mails  to  avoid  mis- 
takes and  loss. 

(5)  Those  issued  by  individuals.  These  include  all  forms 
of  commercial  drafts.  They  may  be  divided  into  two  general 
classes  :  (1)  Documentary  bilU^  with  shipping  receipts,  bills 
of  lading,  insurance  policies,  etc.,  attached  as  evidence  that 
the  drawer  of  the  draft  has  performed  his  part  of  the  trans- 
action ;   (2)    Clean  hills^  having  no  documents  attached. 

354.  As  in  domestic  exchange  the  cost  of  foreign  exchange 
should  never  exceed  the  cost  of  shipping  the  actual  money. 
The  banks,  through  which  most  of  the  exclianges  are  made 
either  directly  or  indirectly,  maintain  the  rates  by  actual 
shipments  of  money,  usually  gold. 

355.  The  par  of  exchange  between  any  two  countries  is 
based  on  the  value  of  the  pure  metal  (gold  or  silver)  con- 
tained in  the  unit  coin  of  any  country,  expressed  in  terms 
of  the  coin  of  another  country.     For  example :  The  United 


FOREIGN  EXCHANGE  211 

States  dollar  (as  a  unit  of  money)  contains  23.22  grains  of 
fine  gold  ;  English  pound  sterling  contains  113.0016  grains. 
The  par  of  exchange  between  the  United  States  and  Eng- 
land is,  therefore,  113.0016  ^23.22,  or  X  1  =  84.8665.  For 
the  values  of  foreign  money  see  page  241.  The  most  im- 
portant exchange  rates  are  quoted  as  follows : 

England £  =$4.8665 

France $1  =  F.  5.18^ 

Germany M.  4  =  |  .95 

Holland 1  guilder  =  $  .40 

356.  Indirect  exchange  (called  arbitrage)  is  used  when 
the  quotations  are  such  that  it  becomes  cheaper  to  send 
money  to  London  via  Paris  than  to  send  it  direct. 

Suppose  the  quotations  are  as  follows  : 

London  exchange  in  New  York     ......£  1  =  $4.88J 

London  exchange  in  Paris £  1  =  F.  25.10 

Paris  exchange  in  New  York |1  =  F.  5.23 

EXERCISES 

1.  I  wish  to  send  $  50  by  money  order  to  each  of  the  fol- 
lowing countries  :  Germany,  England,  France,  and  Holland. 
For  how  much  will  each  order  read,  in  terms  of  the  money 
of  the  country  to  which  it  is  to  be  sent  ? 

2.  Exchange  being  at  par,  what  will  be  the  cost  of  a  draft 
on  London  for  £  62  98.  Id.  ? 

3.  What  will  be  the  cost  of  a  draft  on  Paris  for  F.  1000, 
exchange  being  quoted  at  t^q  %  premium  ? 

4.  What  will  be  the  cost  of  a  letter  of  credit  for  $  5000  ? 
Of  travelers'  checks  for  $  800  ? 

5.  What  will  it  cost  to  cable  $  400  to  London,  the  cable 
rate  being  S3  ?  If  London  exchange  is  quoted  at  par,  what 
amount  in  English  money  will  be  transferred  ? 


212  EXCHANGE 

6.  How  large  a  draft  can  be  bought  on  Denmark  for 
$2000?  (See  table  in  appendix.)  On  the  Pliilippine 
Islands  for  1 125  ?     On  Sweden  for  11285.67  ? 

7.  A  firm  owes  £283  5«.  6d.  in  London,  F.  16,723  in 
Paris,  and  M.  4933  in  Germany.  Quotations  at  the  time  of 
sending  are  as  follows  : 

Sterling $4.8595 

Francs 5.20 

Marks 94^ 

What  will  be  the  amount  of  the  firm's  check  to  purchase 
the  exchange  ? 

8.  What  will  be  the  cost  of  a  draft  on  the  City  of  Mexico 
for  2550  pesos  ? 

9.  Will  it  be  cheaper  to  send  £  1000  to  London  direct  or 
to  convert  the  money  into  Paris  exchange  and  have  it  con- 
verted into  pounds  and  sent  to  London  ?  If  so,  how  much 
cheaper?     (Use  quotations  in  §  356.) 

10.  What  is  the  value  of  a  bill  of  exchange  on  Paris  for 
F.  7160,  at  5.18^ 

11.  If  exchange  on  Berlin  is  at  par,  what  will  be  the  cost 
of  a  bill  of  exchange  for  M.  3750  ? 

12.  How  much  English  money  should  a  traveler  receive 
for  a  travelers'  check  for  1 20  ?     How  much  French  money  ? 

13.  I  hold  a  London  acceptance  for  <£  112  8*.  lOd.,  due  in 
45  da.  If  money  is  worth  4%,  and  the  collecting  charge  is 
J  %,  how  much  can  I  get  for  the  acceptance  at  my  banker's  ? 

14.  How  much  German  money  would  a  traveler  receive 
for  a  letter  of  credit  for  X  200  ? 


15.    What  will  be  the  cost  of  a  letter  of  credit  for  £  100 


PARTNERSHIP 

357.  A  partnership  is  an  association  of  two  or  more  persons 
for  business  purposes. 

358.  The  profits  or  losses  are  shared  according  to  agree- 
ment. 

359.  The  capital  of  a  firm  is  its  total  investment. 

360.  The  resources  of  a  firm  are  its  total  investment  plus 
all  debts  or  obligations  owing  to  the  firm. 

361.  The  liabilities  of  a  firm  are  the  total  debts  or  obliga- 
tions to  others. 

362.  The  excess  of  the  resources  of  a  firm  over  its  lia- 
bilities is  its  present  worth ;  the  excess  of  its  liabilities  over 
its  resources  is  its  insolvency. 

363.  The  net  gain  is  the  excess  of  gains  over  losses. 

364.  Tlie  net  loss  is  the  excess  of  losses  over  gains. 

365.  To  find  what  part  of  the  profit  each  partner  receives. 

The  capital  employed  in  a  business  partnership  is  f  10,000, 
of  which  A  furnishes  16000,  and  B  furnishes  14000.  What 
part  of  any  profit  should  each  receive  ? 

A  has  invested  y\  (_6_o_o_o_.^  ^f  the  capital;  hence  he  re- 
ceives -^Q,  or  -|  of  the  profits. 

B  has  invested  |  of  the  capital ;  hence  he  receives  |  of  the 
profits. 

If  the  profits  should  be  f  2000,  A  would  receive  |  of  $2000, 
or  11200  ;  B  would  receive  f  of  12000,  or  #800. 

213 


214  PARTNERSHIP 

EXERCISES 

1.  A,  B,  and  C  form  a  partnership,  agreeing  to  share  gains 
and  losses  according  to  the  amount  of  their  investments. 
A  invests  14000,  B  85000,  and  C  $6000.  Their  gain  the 
first  year  is  ilOOO.     Find  the  present  worth  of  each. 

2.  A  and  B  have  a  joint  capital  of  $15000.  At  the 
end  of  3  yr.  their  present  worth  is  $21000.  What  is  each 
partner's  gain  if  they  share  equally  ? 

3.  D  invested  $4000  and  E  $5000  in  a  business.  At  the 
end  of  one  year  their  resources  amount  to  $18000,  their  lia- 
bilities to  $3000.     Find  each  partner's  present  worth. 

4.  Three  men  invest  $3000,  $4000,  and  $  5000,  respec- 
tively, in  a  business.  They  agree  to  share  gains  and  losses 
according  to  investment.  At  the  end  of  one  year  their 
present  worth  is  $  8000.     What  was  each  man's  loss  ? 

5.  Jones,  Smith,  and  Deliver  engage  in  business  and  agree 
to  share  gains  and  losses  according  to  investment.  Jones 
invests  $10,000,  Smith  $12,000,  and  Doliver  $13,000.  At 
the  end  of  the  first  year  their  ledger  accounts  were  as  follows: 
Merchandise,  gain  $  10,000  ;  patents,  gain  $  1000 ;  expense, 
loss  $2500;  real  estate,  gain  $1858.75;  equipment,  loss 
$875  ;  interest,  loss  $  200.50.  What  is  each  partner's  pres- 
ent worth,  and  what  per  cent  did  he  make  on  his  investment  ? 

6.  On  Jan.  1,  1911,  A  invests  $5000  in  business.  April 
1,  1911,  B  puts  $4000  in  the  same  business.  Jan.  1,  1912, 
their  ledger  shows  a  gain  of  $2000.  How  much  does  each 
partner  gain,  if  they  share  according  to  the  amount  of  the 
investment  and  length  of  time  it  was  invested  ?  [A  invests 
$  5000  for  12  mo.,  which  is  the  same  as  $  60,000  ($  5000  x  12) 
for  1  mo.  B  invests  $4000  for  9  mo.,  which  is  the  same  as 
$36000  ($4000  X  9)  for  1  mo.  Then  A's  share  is  f  of 
the  profits.] 


RAILROAD   RATES 

366.  Railroad  rates  are  of  two  kinds,  class  and  commod- 
ity. Class  rates  are  applied  to  all  kinds  of  shipments,  whether 
in  carload  lots  or  less,  and  the  rates  are  fixed  at  a  certain 
price  per  100  lb.  All  articles  of  commerce  are  classified  in 
each  "  freight  territory  "  by  a  commission,  which  publishes 
the  result  of  its  work  in  the  form  of  a  freight  classification. 
A  joint  rate  commission,  made  up  of  representatives  of  all 
railroads  in  the  territory,  meets  and  fixes  the  rates  to  apply 
for  each  class,  subject  to  the  sanction  of  the  Interstate  Com- 
merce Commission.  These  rates  are  published  in  what  is 
known  ^^  'd  freight  tariff. 

367.  Commodity  rates  are  applied  to  certain  kinds  of 
heavy  freight,  usually  in  carload  lots.  Among  the  articles 
which  get  special  commodity  rates  are  :  coal,  coke,  ice,  rough 
stone,  lumber,  grain  and  grain  products,  iron  ore,  and  arti- 
cles of  iron  and  steel  manufacture.  In  the  case  of  some  of 
these  the  rate  is  based  on  100  lb.  as  the  unit,  on  others  the 
rate  is  so  much  per  barrel,  while  on  most  of  them  the  ton  is 
the  basis  for  the  rate.  Among  the  commodities  rated  by 
the  short  ton  (2000  lb.)  are  :  rough  stone,  sand,  ice,  coal, 
coke,  and  paving  brick.  Iron  ore  and  articles  of  iron  and 
steel  manufacture  are  rated  by  the  long  ton  (2240  lb.). 

368.  Carload  shipments  must  be  loaded  by  the  shipper 
and  unloaded  by  the  consignee,  but  the  railroad  company 
switches  the  car  to  whatever  siding  is  most  convenient. 
Less-than-carload  shipments  are  handled  by  the  employees 
of  the  railroads.      Carload  rates  are   always  lower  for  the 

215 


216  RAILROAD   RATES 

same  article  than  the  less-than- carload  rates,  but  are  always 
based  on  a  certain  specified  minimum  weight;  for  instance,  if 
a  shipper  has  25000  lb.  of  canned  goods  and  the  minimum 
weight  is  30,000  lb.,  he  will  have  to  pay  freight  on  30,000  lb. 
in  order  to  get  the  benefit  of  the  carload  rate.  If  he  has 
over  30,000  lb.,  he  pays  freight  on  the  actual  weight. 

EXERCISES 

1.  A  shipment  of  sixth -class  freight  moved  from  Parkers- 
burg,  W.  Va.,  to  Syracuse,  N.  Y.  The  rate  was  12J  ^  per 
100  lb.  and  the  consignment  weighed  240,000  lb.  What 
were  the  freight  charges  ? 

2.  What  is  the  fifth-class  rate  from  Chicago  to  Richmond, 
Va.,  when  a  shipment  weighing  4400  lb.  costs  f  118.80  for 
transportation  ? 

3.  The  all-rail  rate  from  Columbus,  Ohio,  to  Provi- 
dence, R.  I.,  is  43|y  per  100  lb.  for  third-class ;  the  rail-aiid- 
water  rate  between  these  points  for  the  same  class  is  41  ^  per 
100  lb.  How  much  will  a  man  save  by  forwarding  a  third- 
class  shipment  weighing  12500  lb.  by  rail-and-water  route  ? 

SuGGKSTiON.     Is  it  necessary  to  find  full  charges  by  separate  routes? 

4.  In  the  official  classification,  automobiles  by  carloads  are 
rated  at  110%  of  first-class  rate,  minimum  weight  10,000  lb. 
The  first-class  rate  between  Vincennes,  Ind.,  and  Utica, 
N.  Y.,  is  70^  per  100  lb.  What  will  it  cost  to  forward  a 
shipment  of  automobiles  weighing  11,250  lb.  between  these 
two  points  ? 

5.  A  druggist  in  Bluefield,  W.  Va.,  received  a  consign- 
ment of  toilet  soap  from  Cincinnati,  Ohio,  rated  at  35  ^  per 
100  lb.  He  notified  the  freight  agent  that  tliere  was  an  error 
in  the  freight  rate,  which  should  have  been  27^^  per  100  lb. 
The  agent  refunded  -$1.80.     What  did  the  soap  weigh? 


RAILROAD  RATES  217 

6.  The  rate  on  canned  vegetables  in  less-than-carload 
lots,  from  Wheeling,  W.  Va.,  to  Baltimore,  Md.,  is  22  j^  per 
100  lb.  The  carload  rate  is  fifth-class,  or  15^  per  100  lb., 
but  the  shipment  is  charged  on  a  basis  of  30,000  lb.  mini- 
mum weight.  A  firm  in  Wheeling  has  a  shipment  of  canned 
vegetables  weighing  22,000  lb.  Should  it  be  billed  as  a 
carload  lot,  or  less-than-carload  shipment?  How  much 
cheaper  is  this  way? 

7.  A  shipment  of  first-class  freight  weighing  8000  lb. 
moved  from  Cleveland,  Ohio,  to  Richmond,  Va.,  via  C.  A.  &  C. 
and  N.  &  W.  Rys.  The  C.  A.  &  C.  received  20  %  of  the  rate 
and  earned  $8.72  for  hauling  the  shipment  from  Cleveland 
to  Columbus,  Ohio.  What  is  the  first-class  rate  from 
Cleveland,  Ohio,  to  Richmond,  Va.? 

8.  A  consigned  40,000  lb.  of  baled  hay  to  B  at  f  18  per 
ton,  allowing  B  to  deduct  the  amount  of  the  freight  charges 
from  the  invoice.  A  got  8330  from  B.  What  was  the 
freight  rate? 

9.  The  fourth-class  rate  from  Columbus,  Ohio,  to  New 
York  is  27  j^  per  100  lb.,  and  the  third-class  rate  is  38J^ 
per  100  lb.  By  mistake  the  rate  clerk  applied  the  third- 
class  rate  to  a  shipment  which  should  have  been  rated  at 
fourth-class.  The  delivering  road  corrected  the  error  and 
refunded  the  consignee  116.10.  How  much  did  the  ship- 
ment weigh  ? 

10.  The  first  four  class  rates  from  Buffalo,  N.  Y.,  to 
Seattle,  Wash.,  are  13.60,  $3.10,  $2.60,  $2.20  per  100  lb., 
respectively,  governed  by  the  western  classification.  This 
classification  makes  shoes  first-class,  leather  in  bags  second- 
class,  and  last  blocks  fourth-class.  What  are  the  freight 
charges  on  the  following  shipment  between  these  two  points  : 
1  bx.  shoes,  80  lb.  ;  1  bag  leather,  120  lb.;  1  bbl.  last  blocks, 
150  lb.? 


218  RAILROAD  RATES 

11.  The  carlx)ad  rate  on  flour  from  Minneapolis,  Minn.,  to 
Tacoma,  Wash.,  is  90^  per  100  lb.,  minimum  weight  56000  lb. 
The  less-than-carload  rate  is  S1.83  per  100  lb.  Washburn, 
Crosby  &  Co.  have  a  consignment  of  150  bbl.  of  Gold  Medal 
flour  to  ship  to  Tacoma.  Should  they  bill  it  as  a  carload 
or  less-than-carload  shipment?  How  much  cheaper  is  this 
way? 

12.  A  farmer  in  Cheyenne,  Wyo.,  ordered  a  wagon, 
a  hay  rake,  and  a  corn  planter  from  a  firm  in  Milwaukee, 
Wis.  When  these  are  taken  apart  and  tied  in  bundles,  the 
western  classification  makes  wagons  first-class,  rakes  second- 
class,  and  corn  planters  third-class.  The  wagon  weighed 
800  lb.,  the  rake  350  lb.,  and  the  corn  planter  500  lb.  The 
rates  for  the  first  three  classes,  Milwaukee  to  Cheyenne,  are 
i3.05,  #2.60,  .f  2.20  per  100  lb.  How  much  did  he  have  to 
pay  for  his  shipment? 

13.  The  rate  on  flour  carloads  from  Indianapolis,  Ind., 
to  Wilmington,  N.  C,  is  made  10|^^  per  100  lb.  to  Kenova, 
W.  Va.,  and  46  ^  per  bbl.,  Kenova  to  Wilmington.  A  car- 
load of  flour  moved  from  Indianapolis  to  Wilmington. 
What  were  the  transportation  charges? 

14.  A  farmer  wants  to  move  from  Logansport,  Ind.,  to 
Columbia,  S.  C,  and  Jias  some  live  stock  to  ship  with  his 
household  goods.  The  rate  is  made  35  ^  per  100  lb.  from 
Logansport,  Ind.,  to  Cincinnati,  official  classification, minimum 
weight  12000  lb.;  and  53^  per  100  lb.  from  Cincinnati  to 
Columbia,  S.  C,  southern  classification,  minimum  weight 
24000  lb.  The  shipment  weighed  18000  lb.  What  are  his 
freight  charges  for  moving? 


PARCEL  POST 

369.  The  Parcel  Post  Act  of  Congress,  which  went  into 
effect  on  Jan.  1,  1913,  provides  for  the  transportation  in 
the  mails  of  merchandise  at  low  rates. 

The  accompanying  table  gives  the  rates  provided  by  law  : 

Table  op  Rates 


First 

Zone 

Second 

Zone, 

50  TO 

150 

Mi, 

Third 
Zone, 

150  TO 
300 
Mi. 

Fourth 

Zone, 

30(»  TO 

600 

Mi. 

Fifth 
Zone, 
600  '10 
1000 
Mi. 

Sixth 
Zone, 
1000  to 

1400 

Mi. 

Sev- 
enth 
Zone, 

1400  TO 

1800 
xMi. 

KwillTH 

ZorE, 

Weight 

Local 
rate 

Zone 

rate,  50 

mi. 

ALL 

OVER 

1800 
Mi. 

lib. 

10.05 

10.05 

10.05 

$0.06 

$0.07 

$0.08 

$0.09 

$0.11 

$0.12 

2  1b. 

.06 

.06 

.06 

.08 

.11 

.14 

.17 

.21 

.24 

3  1b. 

.06 

.07 

.07 

.10 

.15 

.20 

.25 

.31 

.36 

4  1b. 

.07 

.08 

.08 

.12 

.19 

.26 

.33 

.41 

.48 

6  1b. 

.07 

.09 

.09 

.14 

.23 

.32 

.41 

.51 

.60 

6  1b. 

.08 

.10 

.10 

.16 

.27 

.38 

.49 

.61 

.72 

7  1b. 

.08 

.11 

.11 

.18 

.31 

.44 

.57 

.71 

.84 

8  1b. 

.09 

.12 

.12 

.20 

.35 

.50 

.66 

.81 

.96 

9  1b. 

.09 

.13 

.13 

.22 

.39 

.56 

.73 

.91 

1.08 

10  1b. 

.10 

.14 

.14 

.24 

.43 

.62 

.81 

1.01 

1.20 

111b. 

.10 

.15 

.15 

.26 

.47 

.68 

.89 

1.11 

1.32 

20  1b. 

.15 

.24 

.24 

.44 

.83 

1.22 

1.61 

2.01 

2.40 

50  1b. 

.30 

.54 

.54 

The  local  rate  is  applicable  to  parcels  intended  for  delivery 
at  the  office  of  mailing  or  on  a  rural  route  starting  therefrom. 

370.  Under  the  parcel  post  act  the  country  is  divided 
into  units.  Each  unit  is  a  quarter  of  a  quadrangle  formed 
by  meridians  of  longitude  and  parallels  of  latitude. 

219 


220  PARCEL  POST 

371.  The  average  length  of  the  quadrangles  north  and 
south  is  69  mi.,  their  average  width  east  and  west  is  54 
mi.  The  unit,  therefore,  is  about  34|  mi.  long  (north  and 
south)  and  27  mi.  wide  (east  and  west),  with  an  area  of  a 
little  over  930  sq.  mi. 

372.  Each  of  the  6000  (approximately)  units  thus  estab- 
lished is  the  center  of  a  system  of  eight  zones.  The  first 
zone,  called  the  50-mi.  zone,  consists  of  the  unit  itself  and 
its  eight  contiguous  units. 

373.  The  limit  of  weight  for  packages  for  local  delivery 
and  for  delivery  at  other  post  offices  within  the  first  and 
second  zones  is  50  lb.  The  limit  of  weight  for  delivery  in 
other  than  the  first  and  second  zones  is  20  lb. 

EXERCISES 

1.  What  will  it  cost  to  send  a  7-lb.  package  to  a  point  in 
the  300-mi.  zone  ?     One  weighing  9  lb.  ? 

2.  How  far  (into  what  zone)  can  a  package  weighing 
3  lb.  be  sent  for  25  ^  ?  for  15  ^  ?  for  36  i  ? 

3.  A  mail-order  house  sent  out  in  one  day  820  2-lb. 
parcels.  556  of  these  went  into  the  50-mi.  zone,  234  into 
the  150-mi.  zone,  and  30  into  the  300-mi.  zone.  What  post- 
age was  paid  on  all  of  them  ? 

4.  How  much  will  it  cost  to  send  a  20-lb.  package  95 
mi.? 

5.  Find  the  cost  of  sending  5  11-lb.  packages  into  the 
fifth  zone. 


MISCELLANEOUS  PROBLEMS 

Group  1 
Find  the  tax  on  the  following : 

1.  18765  at  .0091. 

2.  12300  at  4  mills  on  the  dollar. 

3.  11400  at  .0126. 

4.  $6800  at  11.75  per  -f  100. 

5.  13750  at  1.871%. 

6.  The  assessed  valuation  of  a  town  is  $3,250,000,  and 
a  property  owner  pays  $44.85  on  property  assessed  at  $3900. 
What  is  the  total  amount  raised  by  taxation  ? 

7.  A's  property,  assessed  at  $16000,  is  taxed  11  mills 
on  the  dollar.  By  paying  his  taxes  promptly  he  secured  a 
discount  of  1  %  from  the  amount.     How  much  does  he  pay  ? 

8.  What  is  the  duty  on  2200  T.  of  hay  at  $4  per  ton? 
on  5000  lb.  of  writing  paper  at  3j^  per  pound?  on  a  yard 
of  silk  ribbon  worth  40  j^  at  50%?  on  a  pair  of  shoes  costing 
$3  at  15%? 

9.  What  is  the  duty  in  United  States  money  on  French 
goods  valued  at  F.  11630  at  30  %  ? 

10.    What  is  the  premium  on  a  life  insurance  policy  for 
$2500,  if  the  premium  on  $10,000  is  $267.10? 

Group  2 

1.  A  building  insured  for  $11,000  is  valued  at  $16,500. 
Under  the  coinsurance  clause,  what  will  the  insurance  com- 
pany pay  in  the  event  of  a  loss  of  $1376.28  ? 

221 


222  MISCELLANEOUS  PROBLEMS 

2.  A  man  has  two  houses  wortli,  respectively,  $4500  and 
'f  3200.  Taxes  are  1|  %,  insurance  is  i  15.50  on  the  first,  and 
$11.20  on  the  second.  The  first  rents  for  $40  per  month; 
the  second,  for  $30.    Which  is  the  better  investment  ? 

3.  An  insurance  company  collects  premiums  amounting  to 
$14,692,308.32  ;  it  pays  out  losses  amounting  to  $5,342,200.20. 
What  is  the  loss  ratio  (percentage  of  losses  to  premiums)  ? 

4.  The  owner  of  a  1913  model  20-horse-power  automo- 
bile costing  $2500  insures  the  machine  (1)  against  injury 
to  persons,  at  $1.20  per  horse  power;  (2)  against  damage 
by  collision,  at  2%  of  the  value  of  the  car;  (3)  against 
damage  to  property,  at  30^  per  horse  power;  (4)  against 
fire  and  theft,  at  2|  %  of  the  value  of  the  car.  What  is  the 
total  amount  paid  by  the  owner  for  such  protection  ? 

5.  A  coal  mining  company  whose  yearly  pay  roll  is 
$30,000  is  insured  against  claims  for  damage  due  to  injury 
to  its  employees  at  $1  per  $100  of  the  pay  roll.  What 
premium  does  the  company  pay  ? 

6.  What  is  the  cost  of  20  shares  of  stock  at  55 J,  broker- 
age \  %  ? 

7.  C  buys  50  shares  of  stock  at  106.  In  18  mo.  time  he 
receives  4  dividends  of  6%  each.  If  money  is  worth  5%? 
how  much  does  he  gain  over  and  above  this  rate  ? 

8.  A  sent  70,000  lb.  of  wheat  to  be  sold  and  the  proceeds 
invested  in.  Southern  Pacific  stock.  The  agent  sold  the 
wheat  for  90^  per  bushel  and  charged  a  2%  commission. 
Southern  Pacific  cost  110,  brokerage  ^  % .  How  many  shares 
did  A  receive,  and  what  surplus  had  he  left  over  ? 

9.  What  is  the  rate  of  investment  on  Atlantic  and  Pacific 
Railroad  4's  bought  at  83,  brokerage  |  %  ? 

10.  I  receive  $375  every  6  mo.  as  interest  on  Erie  5's. 
If  I  bought  them  at  98|,  plus  |%  brokerage,  how  much  did 
I  invest  ? 


MISCELLANEOUS  PROBLEMS 


223 


Group  3 

1.  The  following  is  the  form  in  which  a  broker  keeps  his 
records  of  a  transaction  made  for  a  customer.  In  this  ac- 
count, the  customer  bought  100  shares  of  New  York  Central 
on  Nov.  5,  at  115.  He  deposited  11000  on  the  transaction, 
the  broker  lending  him  at  6%  the  amount  necessary  to  make 
the  purchase.  When  the  stock  is  sold,  the  customer  is 
credited  with  the  amount  of  the  sale,  interest  is  charged, 
and  the  balance  is  credited  to  the  customer. 


Dr. 

Ck. 

Nov.    5 

100  N.Y.  Cent.  115 
Com.  buying 

$11500 
12 

50 

Nov.    5 

Cash 

$1000 

Nov.  20 

Com.  selling 
Tax  selling 

12 
2 

50 

Nov.  20 

100  N.Y.  Cent.  117 
Int.  on  $1000  Nov. 

11700 

Int.  on  §11,512.50 

5  to  Nov.  20 

2 

50 

Nov.  5  to  Nov.  20 

28 

78 

• 

Balance 

1146 

72 

$  12702 

50 

$12702 

50 

The  profit  in  the  transaction  is  the  customer's  balance 
($1146.72)  minus  his  cash  deposit  (11000),  or  1 146.72. 

Note.  Interest  is  charged  on  the  full  amount  of  the  purchase,  and 
credited  on  cash  deposit.     For  tax  (|2)  see  note,  page  200. 

Using  the  above  as  a  model,  make  and  fill  in  forms  for  the 
following  transactions.  Compute  interest  at  5%.  Tax,  2j^ 
per  share  on  sales. 


Date  Bought 

Stock 

Price 

Amount 

Cash 
Uep. 

Date  Sold 

Price 

Amount 

2. 

Aug.    3 

20  P.  Coal 

23^ 

1100 

Oct.   18 

251 

3. 

May  10 

100  U.  S.  Steel 

75i 

800 

Sept.  20 

78 

4. 

Jan.  14 

50  Gen.  Elec. 

180 

1200 

Feb.  19 

192 

5. 

Mar.    2 

75  Amer.  Loco. 

4U 

375 

Mar.  22 

41i 

6. 

Dec.  10 

200  So.  Pac. 

1091 

5000 

Dec.  20 

111 

224  MISCELLANEOUS  PROBLEMS 

7.  A  bank  bid  #831.58  above  par  for  an  entire  issue  of 
il5000  5%  school  bonds.  What  return  does  the  invest- 
ment make  the  bank  ? 

8.  A  corporation  has  outstanding  86,000,000  of  6%  pre- 
ferred, and  'f  12,000,000  common  stock.  Its  net  earnings  for 
the  year  are  11,131,885.  What  per  cent  dividends  will  the 
common  stock  earn  ? 

9.  A  man  having  83000  to  invest  buys  12  shares  of 
stock  at  400,  borrowing  enough  additional  on  the  stock  as 
collateral  to  make  the  purchase.  If  he  pays  5%  on  his  loan, 
and  the  stock  pays  25  %  dividends,  what  per  cent  is  he  mak- 
ing on  his  investment  ?     (Par  value,  8100.) 

10.  Which  is  the  better  investment,  100  shares  of  6%  pre- 
ferred stock  at  107|,  or  50  shares  of  12%  common  at  214|? 
(Brokerage,  ^%.) 

Group  4 

1.  A  salesman  sells  in  one  year  1128,466.73  worth  of 
goods  on  a  5%  commission.  His  expenses  for  the  year  are 
$3246.80,  and  he  pays  8117.43.  taxes  and  8245.48  insurance. 
He  buys  10  shares  of  bank  stock  direct  from  the  owner  at 
8165  per  share,  and  sete  aside  8263.63  for  a  cliecking  account 
at  the  bank.  If  he  deposits  the  rest  of  his  year's  income  in 
a  bank  at  3J%,  what  interest  will  it  bring  him  annually  ? 

2.  I  discount  a  10-day  acceptance  for  82500  at  5|  %  and 
use  the  proceeds  in  buying  a  telegraph  money  order.  If  the 
10-word  rate  is  60  ^  what  amount  is  available  to  the  person 
receiving  the  order  ? 

3.  A  draws  on  B  at  sight  for  8162.57  with  exchange. 
To  meet  the  draft  B  borrows  the  money  at  his  bank  at  6% 
for  60  da.  What  is  the  amount  of  B's  note  when  due  ? 
(Exchange,  20^.) 

4.  A  corporation  issues  875000  6%  bonds,  which  it  is 
forced  to  sell  at  87.     In  paying  the  interest  on  its  bonded 


MISCELLANEOUS  PROBLEMS  225 

indebtedness  what  rate  does  it  pay  on  the  money  actually 
received  for  the  bonds  ? 

5.  A  buys  100  shares  of  stock  at  27 1  and  sells  them  at 
30.  Allowing  brokerage  of  ^%  on  each  transaction,  how 
much  does  he  gain  ? 

6.  The  firm  X,  Y,  Z  makes  a  gross  profit  in  one  year  of 
8  25,004.  They  charge  oif  $■  1484  to  depreciation  on  machin- 
ery, 8675  to  depreciation  on  trade  mark,  and  pay  $6160  for 
general  expenses  and  wages.  If  the  three  members  of  the 
firm  are  equally  interested  in  the  business,  how  much  will 
each  receive  as  his  share  of  the  net  profits  ? 

7.  A  borrows  815000  on  his  note  at  7  %.  To  secure  the 
note  he  takes  out  a  life  insurance  policy  for  8  18000  at  8 14.62 
per  thousand,  annual  premium.  The  815000  is  invested  in 
a  third  interest  in  a  business  which  shows  a  profit  at  the  end 
of  the  year  of  33|^  %.  What  is  the  net  rate  of  income  on  the 
investment  ? 

8.  Find  the  proceeds  on  the  following  sight  drafts: 

Face  of  Draft  Collection  and  Exchange 

$28.63  10^ 

162.45  •                  i% 

4216.53  •                        ■           5V7o 

6.20  6^ 

683.10  io/o 

1370.64  J^o/o 

9.  Find  the  cost  of  a  bill  of  exchange  for  : 

-£  362  lis.  M if  1  £  =  $4.8725 

F.3624 if  F.  5.161  =  11 

M.  11360 if  M.  4  =  $.95| 

10.  A  bond  issue  of  8 1,000,000  was  oversubscribed  3|^  times ; 
that  is,  the  subscriptions  amounted  to  83,500,000.  If  each 
subscriber  receives  bonds  in  proportion  to  his  subscription, 
what  did  the  subscriber  receive  who  asked  for  8 14000  worth  ? 

BUS.    ARITH. 15 


226  MISCELLANEOUS  PROBLEMS 

Group  5 

1.  How  much  will  I  receive  for  a  90-day  acceptance  for 
$  350,  discounted  at  6  %,  exchange  {%? 

2.  How  much'  will  it  cost  to  telegraph  $125  from  Cleve- 
land, Ohio,  to  Nashville,  Tenn.,  the  telegraph  rate  being  60  ^? 

3.  An  importer  buys  £  163  8«.  Sd.  worth  of  goods  on 
which  he  pays  a  duty  of  20  %.  For  how  much  U.  S.  money 
must  he  sell  to  realize  a  profit  of  20  %  of  the  cost  ? 

4.  A  and  B  own  a  business,  A  holding  a  |  interest,  and 
B  a  I  interest.  If  they  sell  a  third  interest  for  $6200,  what 
must  A  and  B  each  receive  in  order  that  A,  B,  and  C  may 
thereafter  be  equally  interested  in  the  business  ? 

5.  A  has  15000  invested  in  a  store,  B  has  '13000,  and  C 
has  12000.  They  decide  to  add  $4000  to  the  capital  em- 
ployed. What  part  of  this  amount  must  each  partner  furnish 
in  order  that  their  relative  interests  may  remain  unchanged  ? 

6.  What  is  the  value  of  a  90-day  acceptance  for  X 112 
Is.  46?.,  London  exchange  being  quoted  at  $4.84|,  discounted 
at  6%? 

7.  An  inventor  holds  100  shares  of  6%  preferred  stock, 
200  shares  of  5%  common,  and  $22000  6%  bonds  of  the 
same  company.     What  is  his  income  ? 

8.  A  bank  capitalized  at  $300,000  has  a  surplus  of 
$317,578.  What  per  cent  dividends  might  be  declared  by 
appropriating  60  %  of  the  surplus  to  such  a  purpose  ? 

9.  A  company  purchased  M.  18000  worth  of  German 
goods  on  which  it  paid  $450  duty  and  $106.85  freight.  The 
goods  were  sold  for  $6320,  less  2%.     What  was  the  profit? 

10.  A,  holding  B's  note  for  $270  with  interest  for  4  mo. 
at  7  %,  draws  on  B  through  the  First  National  Bank  of  Burt, 
Iowa,  at  sight  for  the  full  amount.  B's  place  of  business 
is  Denver,  Col.     Write  the  draft. 


REVIEW  PROBLEMS 


ORAL   EXERCISES 


1.  34  X  11 

2.  45  X  200 

3.  93  X  97 

4.  472  X  300 

5.  67  X  11 

6.  4532x11 

7.  6469  X  150 

8.  9540  X  125 


9.     61  X 


10.  51  X  5J 

11.  450  X  450 

12.  6ix6i 

13.  9ix9J 

14.  425  X  625 

15.  625  X  4.25 

16.  8ix8J 

17.  7fx7f 

18.  425  X  8250 

19.  91x91 

Find  the  following: 

58.  10  %  of  280 

59.  20  %  of  60 

60.  48  %  of  175 


20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 
29. 
30. 
31. 
32. 
33. 
34. 
35. 
36. 
37. 
38. 

61. 
62. 
63. 


325  X  925 
750  X  750 
290  X  150 
756  X  175 
35  X  35 
.95  X .65 
8.5  X  750 
121  X  1.25 
75x25 
10|  X  lOi 
6|x6f 
5J  X  5^ 
2f  x2| 
925  X  725 
81  X  8.31 
4x1375 

5|^6 
foff 


16|  %  of  660 

1081%  of  240 

92%  of  150 
227 


39.  424-25 

40.  7650-50 

41.  60 -^f 

42.  725^1.331 

43.  125-^1 

44.  452 -.161 

45.  7840-125 

46.  475 -^f 

47.  5896-^.161 


48.  .12i  =  ? 

49.  .081=? 

50.  .331=? 

51.  .871  =  ? 

52.  .58^  =  ? 

53.  1.331  =  ? 

54.  .55|  =  ? 

55.  .561  =  ? 


56. 
57. 


06J 


,621  =  9 


64.  .2%  of  640 

65.  .3%  of  5 

66.  150%  of  500 


228  REVIEW  PROBLEMS 

67.  .l%of.l  69.    .08|ofl2  71.    a3i%of3| 

68.  .01%  of  740        70.    16|%of45        72.    I  %  of  36 
73.    56  J  %  of  48         74.    12  is  4  %  of  what  number  ? 

75.  24  is  41|  %  of  what  number  ? 

76.  .25  is  80%  of  what  number? 

77.  .83^  is  20  %  of  what  number? 

78.  4  is  I  %  of  what  number? 

79.  35  is  6|  %  of  what  number? 

80.  .621  is  83J%  of  what  number? 

81.  Reduce  |  to  24ths.       83.    Reduce  |J  to  lowest  terms. 

82.  Reduce  f  to  21sts.        84.    From  |  take  |. 

85.  From  /j  take  -^. 

Find  the  interest  at  6  %  : 

Pkinoipal  Tihb 

86.  i400  Syr. 

87.  250  120  da. 

88.  325  80  da. 

89.  720  1  mo.  10  da. 

90.  600  40  da. 

91.  A  man  had  ^2000  and  spent  20%  of  it.  How  much 
money  had  he  left  ? 

92.  Owning  a  farm  of  420  A.,  I  sold  16|%  for  84900. 
What  price  per  acre  did  I  receive  ? 

93.  Owning  60%  of  the  stock  of  a  manufacturing  com- 
pany, T  sold  20%  of  my  share  for  $2400.  What  was  tlie 
value  of  the  entire  stock  ?  of  my  share  ? 

94.  I  sold  a  horse  for  $  200,  which  was  at  a  loss  of  20  % 
of  the  cost.     Find  the  cost. 

95.  How  many  times  can  36  be  subtracted  from  300  ? 

96.  A  baseball  team  wins  14  games  and  loses  10.  What 
is  its  per  cent  of  games  won  ? 


REVIEW  PROBLEMS 


229 


97.  A  catalogue  lists  an  article  at  145,  but  allows  25% 
and  20  %  off.     Find  the  net  selling  price. 

98.  Brown  gained  |500  the  first  year  and  after  adding 
his  gain  to  his  investment,  lost  \  of  the  amount  the  second 
year.     He  then  had  $1800.     How  much  had  he  at  first  ? 

99.  A  invests  1600  and  B  $800.  Their  gain  is  8300. 
What  should  each  receive  ? 

100.    What  will  it  cost  to  send  a  7-pound  parcel  into  the  150- 
mile  zone  by  parcel  post  ? 


WRITTEN 

EXERCISES 

1.  Add  and  check  : 

2.  Add  and  check 

2875648 

9572674 

1792559 

8468739 

1624076 

7254927 

9217845 

6248725 

7384957 

9764523 

6294738 

78654 

7549629 

837642 

6872597 

9872937 

827358 

1640735 

75646 

8295439 

198478 

764375 

7354629 

4874062 

6473746 

567432 

1897645 

28739 

735490 

543721 

6487 

17687 

954398 

649586 

2872594 

7468929 

7658 

8295437 

64352 

7804 

230 


REVIEW  PROBLEMS 


3.    Add  and  subtract  alterDately 

8972549 
2762597 


2437538 


7642973 


297364 


4.  Add: 

687.25 

-384.20 

72.85 

16.92 

140.62 
45.07 
83.98 


8549321 


5432976 


849278 


5.    Add  by  the  balancing  account  method  and  check : 


Balance 

Check 

Deposits 

Balance 

A 
B 
C 
D 
E 
F 

985.72 
487.68 

95.98 
168.75 

72.59 
354.86 

342.89 

159.20 

20.07 

68.92 

14.09 

215.96 

58.72 
268.73 

75.00 
934.58 

54.72 
134.17 



Total 

6.    Find  the  balance  : 

Dr. 

Or. 

12874.58 

11975.62 

1784.63 

8573.74 

8873.19 

175.14 

982.73 

1354.05 

3214.95 

938.15 

REVIEW  PROBLEMS 


231 


7.    Multiply  and  check 

78549872 
927 


8.    Multiply : 

147268 
9154 


9.    Find  the  G.  C.  D.  of  24,  132,  144. 

10.  Find  the  L.  C.  M.  of  81,  120,  117. 

11.  Add: 

765.641 

421 

678. 6  J^ 
4572. 68^ 

62.141 
759f 

12.  Multiply  534|  by  8.24J. 

13.  Divide  7825963^1  by  .16f. 

14.-   Multiply  18  bu.  3  pk.  2  qt.  by  12. 

15.    Extend  and  foot  the  following  : 


NuMBKR  OF  Pounds 

Article 

Price 

Value 

84000 

12578 

6250 

5348 

28364 

Hay 

Corn 

Oats 

Bran 

Chop 

$  10  per  ton 
80  f  per  bushel 
40  ^  per  bushel 
$18  per  ton 
$30  per  ton 
Total     .     . 

16.  The  hypotenuse  of  a  right  triangle  is  400  ft.,  the  base 
200  ft.,  what  is  its  area? 

17.  Find  the  area  of  a  circle  whose  diameter  is  10  ft. 

18.  What  will  it  cost  to  carpet  a  room  16'  x  18'  x  15',  if 
the  carpet  is  |  of  a  yard  wide,  at  •'^1.50  per  yard? 


232 


REVIEW  PROBLEMS 


19.  At  '$5  per  thousand  what  will  it  cost  to  shingle  a  flat 
roof  150'  X  60',  allowing  850  shingles  to  a  square  ? 

20.  How  many  cords  of  wood  in  a  pile  20'  x  4'  x  8'  ? 

21.  A  commission  merchant  sold  a  carload  of  lumber,  and 
sent  the  owner  ^3564.25,  after  paying  f  70  freight  charges, 
and  retaining  2|  %  commission  for  selling.  What  was  his 
commission? 

22.  A  pay  roll  made  from  time  slips  and  rates  per  hour  as 
shown  below  will  amount  to  how  much? 


• 

Time 

Uatb 

AuorNT 

A 
B 
C 
D 
E 

24  hr. 
40  hr. 
48  hr. 
50  hr. 
40  hr. 

.12^  per  hour 
.14    per  hour 
.20    per  hour 
.17|  per  hour 
.22^  per  hour 
Total    .     .     . 

1! 

23.  What  sum  must  a  man  invest  in  5%  bonds  bought  at 
120  to  give  his  son  an  annual  income  of  ^1200  ? 

24.  A  man  having  money  to  invest  in  bonds  has  a  list  from 
which  he  wishes  to  select  the  investment  most  profitable  to 
him.     The  list  includes  : 

1.  5   %  bonds,  market  price  f  110 

2.  6    %  bonds,  market  price    120 

3.  4   %  bonds,  market  price     100 

4.  4J%  bonds,  market  price      60 

5.  3    %  bonds,  market  price      90 
Which  bonds  should  he  purchase  ? 

25.  A  commission  merchant  sold  for  his  principal  400  bu. 
of  potatoes  at  90^  per  bushel,  and  after  deducting  $3.80  for 
freight,  and  his  commission  of  3  %,  remitted  a  check  for  the 
proceeds.     What  was  the  amount  of  the  check  ? 


REVIEW  PROBLEMS 


233 


26.  I  sold  two  houses  for  18000  each.  On  one  I  gained 
20  %  of  the  cost,  and  on  the  other  I  lost  20  %  of  the  cost. 
Did  I  gain  or  lose  on  the  whole  transaction,  and  how  much  ? 

27.  A  real  estate  dealer  sold  a  house  for  iTOOO  ;  after  pay- 
ing expenses  of  §440,  he  finds  that  his  gain  is  16|%  of  the 
cost.     How  much  did  the  house  cost  him  ? 

28.  Which  is  better  for  the  buyer,  a  discount  series  of  20, 
20,  and  10,  or  25,  15,  and  10,  and  how  much  ? 

29.  An  article  at  §4.50  was  discounted  20%  and  1.80. 
What  was  the  second  rate  of  discount  ? 

30.  How  shall  goods  that  cost  145  be  marked  so  that  a 
discount  of  10%  may  be  made  from  the  marked  price  and 
then  sell  at  a  profit  of  10  %  of  the  cost  ? 

31.  A  lent  B  $900  for  2  mo.  At  the  same  rate,  what 
amount  shall  B  lend  A  for  3  mo.  in  return  for  tlie  accommo- 
dation ? 

32.  On  April  3,  a  carriage  manufacturer  in  Ohio  sells  a 
shipment  to  a  Texas  dealer,  amounting  to  f  850.  He  attaches 
the  bill  of  lading  to  a  60-day  sight  draft  which  he  discounts 
at  his  bank  at  6%.  Allowing  12  da.  before  the  consignee 
can  receive  and  inspect  the  shipment,  and  3  da.  for  return  to 
the  Ohio  bank  after  payment  in  Texas,  what  are  the  proceeds 
of  the  draft,  collection  charges  being  -^^  %  ? 

33.  A  shoe  manufacturer  discounts  at  his  bank  the  follow- 
ing notes  from  out-of-town  customers : 


Face 

Time 

Rate  % 

.$123.45 

240.00 

93.25 

107.70 

90  da. 

•  30  da. 

30  da. 

60  da. 

7  %  from  date 

5i  %  from  date 

6  %  from  date 

6  %  from  date 

234 


REVIEW  PROBLEMS 


What  are  the  proceeds  of  these  notes,  if  the  bank  discounts 
them  at  5  %  ?  (Add  4  days'  time  in  discounting  to  allow  for 
time  in  transit.) 

34.  A  farmer  ships  a  car  containing  38762  lb.  of  pota- 
toes to  a  broker,  who  sells  them  for  82^  per  hundredweight. 
Freight  charges  are  173.20,  and  the  broker  charges  a  com- 
mission of  2  %.     What  amount  is  returned  to  the  farmer? 

35.  The  Detroit  Times  shows  the  following  circulation  for 
one  month : 


MON. 

Tubs. 

Wed. 

Tilt-. 

Fr.. 

Sat. 

Total 

36555 

36302 

36310 

36258 

36338 

36303 

36233 

36500 

36173 

36147 

36668 

38710 

40871 

43005 

43609 

43458 

43351 

35835 

35967 

35881 

36733 

76940 

36514 

36359 

36998 

36198 

36329 

(a)  Find  the  total  circulation  for  each  week. 

(K)  Find  the  total  circulation  for  each  day  in  the  week. 

(c)  Find  the  total  circulation  for  the  month. 

(c?)  What  is  the  average  circulation  per  day? 

(e)  What  day  is  nearest  the  average? 

36.  Which  of  two  salesmen,  A  and  B,  whose  yearly  sales 
are  given  below,  returns  more  profit  to  his  firm  ? 

A  sells  $225,000  worth,  showing  an  average  profit  to  the 
firm  of  11|^%  of  his  sales;  cost  of  collections  \^\%^  selling 
expenses,  $6450. 

B  sells  $260,000  worth  at  an  average  profit  of  10|%  of  his 
sales;  cost  of  collection,  |%,  selling  expenses,  $7200. 

37.  A  company  issues  $100,000  7%  preferred  stock,  and 
$  100,000  of  common  stock.  It  earns  in  one  year  $28,762.20. 
What  amount  can  be  added  to  the  surplus  if  it  pays  11% 
dividends  on  the  common  stock,  and  charges  $3333.33  to 
depreciation  of  plant  and  equipment  ? 


REVIEW   PROBLEMS  235 

38.  If  the  advertising  expense  incident  to  the  sale  of  an 
article  is  i  10,000,  and  this  expense  is  divided  among  manu- 
facturer, jobber,  and  retailer  according  to  the  profits  of  each, 
what  part  will  be  paid  by  each,  if  the  profits  are,  respectively, 
22%,  13%,  and  15%? 

39.  A  merchant  buys  $15000  worth  of  goods  at  2% -10, 
net  60.  How  much  will  he  save  by  borrowing  the  money 
for  30  da.  at  6  %  in  order  to  discount  the  bill  ? 

40.  If  a  retailer  sells  an  article  for  fl2.50,  showing  20% 
profit  on  the  selling  price,  at  what  can  he  afford  to  sell  it  if 
he  is  willing  to  take  only  10  %  profit  on  the  cost  ? 

41.  Find  the  difference  between  simple  interest  and  com- 
pound interest  on  19375  for  10  yr.  at  6  %. 

42.  An  agent  sold  for  his  principal  goods  to  the  amount 
of  110,000,  charging  3  %  commission.  He  invested  the  pro- 
ceeds in  wheat  after  deducting  a  commission  of  2  %  for  buy- 
ing. If  he  paid  90  %  per  bushel  for  the  wheat,  how  many 
bushels  did  he  buy  ? 

43.  The  average  circulation  of  the  Bosto7i  Daily  Post  for 
August  was  418,562,  a  gain  of  59,056  copies  per  day  over 
August  in  the  previous  year.  What  per  cent  of  increase  is 
shown  ? 

44.  In  1912  the  population  of  the  United  States  was  ap- 
proximately 95,000,000.  The  family  expenditures  were  as 
follows : 

Article  Amount 

Food  $8000000000 

Clothing  3000000000 

Intoxicants  2000000000 

Tobacco  1000000000 

Fuel  800000000 

Life  Insurance  600000000 

Furniture  600000000 


236  REVIEW   PROBLEMS 

(a)  What  per  cent  of  the  total  expenditure  was  spent  for 
tobacco  and  intoxicants  combined  ? 

(b)  What  is  the  total  expenditure  on  these  items  for  each 
person  in  the  United  States  ? 

45.  A  dealer  sold  a  buggy  for  i98,  an  advance  of  16|% 
over  the  cost.  If  he  extends  to  the  purchaser  credit  for 
6  mo.  without  interest,  what  was  his  real  per  cent  of  gain, 
money  being  worth  6  %  ? 

46.  An  agent  sells  80,000  lb.  of  wheat  at  90^  per  bushel. 
He  accepts  a  60-day  note,  which,  wlien  discounted  at  5  %, 
pays  the  bill.     What  is  the  face  of  the  note  ? 

47.  A  owes  four  bills  which  he  pays  by  New  York  drafts, 
the  amounts  being  as  follows:  $49.50,  i8?286.75,  $158.76, 
and  $61.10.  If  exchange  is  J%,  what  exchange  does  he 
pay? 

48.  A  buys  goods  to  the  amount  of  $4586.90,  less  3  %  for 
cash.  He  holds  B's  30-day  acceptance  for  $1200,  and  C's 
60-day  note  for  $2256.30  at  5%.  If  A  discounts  the  ac- 
ceptance and  the  note  at  5%,  and  remits  the  full  amount 
of  his  purchase  by  bank  draft,  exchange  being  ^V%'  what 
does  he  save  by  paying  cash  ? 

49.  A  man  has  $25,050  to  invest.  Which  will  yield  the 
more  in  one  year,  Norfolk  and  Western  R.  R.  at  167,  no 
brokerage,  paying  5%  dividends,  or  a  deposit  in  a  savings 
bank  at  3  %  interest  yearly  ? 

50.  A  business  property  is  valued  at  $200,000.  If  the 
owner  pays  1J%  taxes,  and  allows  10%  of  the  earnings  for 
depreciation  of  the  building,  for  how  much  must  he  rent  it 
to  clear  7  %  on  his  investment  ? 


APPENDIX 

THE    METRIC    SYSTEM 

The  metric  system  is  a  decimal  system  of  weights  and 
measures.  The  United  States  Government  requires  the  use 
of  the  metric  system  of  measures  in  all  medical  work  of  the 
navy  and  war  departments,  and  in  the  public  health  and 
marine  hospital  service. 

Linear  Measure 

The  unit  of  linear  measure  is  the  meter. 

Table 
10  milliineters  (mm.)  =  1  centimeter  (cm.) 
10  centimeters  =  1  decimeter  (dm.) 

10  decimeters  =  1  meter  (m.) 

10  meters  =  1  decameter  (Dm.) 

10  decameters  =  1  hectometer  (Hm.) 

10  hectometers  =  1  kilometer  (Km.) 

10  kilometers  =  1  myriameter  (Mm.) 

Square  Measure 

The  unit  of  square  measure  is  the  square  meter  for  small 
areas,  and  the  are  of  100  sq.  m.  for  land  areas. 

Table 
100  square  millimeters  (sq.  mm.)  =  1  square  centimeter  (sq.  cm.) 
100  square  centimeters  =  1  square  decimeter  (sq.  dm.) 

100  square  decimeters  =  1  square  meter  (sq.  m.) 

100  square  meters  =  1  square  decameter  (sq.  Dm.) 

100  square  decameters  =  1  square  hectometer  (sq.  Hm.) 

100  square  hectometers  =  1  square  kilometer  (sq.  Km.) 

237 


238  APPENDIX 

Land   Measure 
The  unit  of  land  measure  is  the  are. 

Table 

100  centares  (ca.)  =  1  are  (a.)  =  100  square  meters 

100  ares  =  1  hectare  (Ha.)  =  10000  square  meters 

Cubic  Measure 
The  unit  of  volume  is  the  cubic  meter. 

Table 

1000  cubic  millimeters  (cu.  mm.)  =  1  cubic  centimeter  (cu.  cm.) 
1000  cubic  centimeters  =  1  cubic  decimeter  (cu.  dm.) 

1000  cubic  decimeters  =  1  cubic  meter  (cu.  m.) 

Wood  Measure 
The  unit  of  wood  measure  is  the  stere. 

Table 

10  decisteres  (ds.)  =  1  stere  (s.)  =  1  cubic  meter 

10  steres  =  1  decastere  (Ds.)  =  10  cubic  meters 

Measure  of  Capacity 

The  unit  of  capacity  for  either  solids  or  liquids  is  the  liter., 
which  is  equal  in  volume  to  1  cu.  dm. 

Table 

10  milliliters  (ml.)  =  1  centiliter  (cl.) 
10  centiliters  =  1  deciliter  (dl.) 

10  deciliters  =  1  liter  (1.) 

10  liters  =  1  decaliter  (Dl.) 

10  decaliters  =  1  hectoliter  (HI.) 

10  hectoliters  =  1  kiloliter  (Kl.) 


TABLES  OF  EQUIVALENTS  239 

Measure  of  Weight 

The  unit  of  weight  is  the  gram^  which  is  the  weight  of  1 
cu.  cm.  of  distilled  water  in  a  vacuum,  at  its  greatest  density 
(39.2°  F.).     It  weighs  15.4324  gr. 

Table 

10  milligrams  (mg.)  =  1  centigram  (eg.) 

10  centigrams  =  1  decigram  (dg.) 

10  decigrams  =  1  gram  (g.) 

10  grams  =  1  decagram  (Dg.) 

10  decagrams  =  1  hectogram  (Hg.) 

10  hectograms  =  1  kilogram  (Kg.) 

10  kilograms  =  1  myriagram(Mg.) 

10  myriagrams  =  1  quintal  (Q.) 

10  quintals  =  1  tonneau  (T.) 

TABLES   OF  EQUIVALENTS 

Linear  Measure 

1  inch  =  2.54  centimeters  1  centimeter  —  .3937  of  an  inch 

1  foot  =  .3048  of  a  meter  1  decimeter   =  .328  of  a  foot 

1  yard  =  .9144  of  a  meter  1  meter  =  1.0936  yards 

1  rod    =  5.029  meters  1  decameter  =  1.9884  rods 

1  mile  =  1.6093  kilometers  1  kilometer  =  .62137  of  a  mile 

Surface  Measure 

1  square  inch  =  6.452  square  centimeters 
1  square  foot  =  .0929  square  meter 
1  square  yard  =  .8361  square  meter 
1  square  rod  =  25.293  square  meters 

1  acre  =  40.47  ares 
1  square  mile  =  259  hectares 

1  square  centimeter  =  .155  square  inch 
1  square  decimeter  =  .1076  square  foot 
1  square  meter  =  1.196  square  yards 
1  are  =  3.954  square  rods 
1  hectare  =  2.471  acres 
1  square  kilometer  =  .3861  square  mile 


240  APPENDIX 

Cubic  Measure 

1  cubic  inch  =  1G.387  cubic  centimeters 
1  cubic  foot  =  28.817  cubic  decimeters 
1  cubic  yard  =  .7(546  cubic  meter 
1  cord  =  3.624  steres 

1  cubic  centimeter  =  .061  cubic  inch 
1  cubic  decimeter  =  .0353  cubic  foot 
1  cubic  meter  =  1.308  cubic  yards 
1  stere  =  .2759  cord 

Measures  of  Capacity 

1  dry  quart       =  1.101  liters  1  liter  =  .908  dry  quart 

1  liquid  quart  =  .9163  liter  1  liter  =  1.0567  liquid  quarts 

1  liquid  gallon  =  .3785  decaliter  1  decaliter   =  2.6417  liquid  gallons 

1  peck  =  .881  decaliter  1  decaliter    =  1.135  pecks 

1  bushel  =  .3524  hectoliter  1  hectoliter  =  2.8377  bushels 

Measures  of  Weight 

1  grain  Troy  =  .0648  gram 
1  ounce  Troy  =  31.104  grams 
1  ounce  avoirdupois  =  28.35  grams 

1  pound  Troy  =  .3732  kilogram 
1  pound  avoirdupois  =  .4536  kilogram 
1  ton  (short)  =  .9072  ton 

1  gram  =  15.432  grains  Troy 
1  gram  =  .03215  ounce  Troy 
1  gram  =  .03527  ounce  avoirdupois 
1  kilogram  =  2.679  pounds  Troy 
1  kilogram  =  2.2046  pounds  avoirdupois 
1  ton  =  1.1023  short  tons 

Convenient  Equivalent  Values 

1  cubic  centimeter  of  water  =  1  milliliter  of  water,  and  weighs  1  gram  = 

15.432  grains 
1  cubic  decimeter  of  water  =  1  liter  of  water,  and  weighs  1  kilogram  — 

2.2046  pounds 
1  cubic   meter  of  water  =  1   kiloliter  of   water,   and  weighs    1    ton  = 

2204.6  pounds 


VALUES  OF  FOREIGN  COINS 


241 


VALUES    OF   FOREIGN    COINS 


Value  in 

Country 

Le(}al  Standard 

Monetary  Unit 

Terms  of 

U.  S. 
Money 

Argentine  Republic      .     . 

Gold 

Peso 

10.9647 

Austria-Hungary     .     .     . 

Gold 

Crown 

.2080 

Belgium 

Gold  and  silver 

Franc 

.1930 

Brazil 

Gold 

Milreis 

.5460 

Canada      

Gold 

Dollar 

1.0000 

Central  American  States: 

Costa  Rica 

Gold 

Colon 

.4650 

British  Honduras     .     . 

Gold 

Dollar 

1.0000 

Nicaragua 

Gold 

Cordova 

1.0000 

Guatemala  .     .     .     .      | 

Honduras    .     .     .     .      [ 

Silver 

Peso 

.4340 

Salvador     .... 

Chile 

Gold 

Peso 

.3650 

China 

Silver 

Tael 

.649  to  .723 

Denmark 

Gold 

Crown 

.2680 

Egypt 

Gold 

Pound  (100  piasters) 

4.9430 

Finland 

Gold 

Mark 

.1930 

France  

Gold  and  silver 

Franc 

.1930 

German  Empire .... 

Gold 

Mark 

.2380 

Great  Britain      .... 

Gold 

Pound  sterling 

4.8065 

Greece 

Gold  and  silver 

Drachma 

.1930 

Italy 

Gold  and  silver 

Lira 

.1930 

Japan   

Gold 

Yen 

.4980 

Mexico 

Gold       ' 

Peso 

.4980 

Netherlands 

Gold 

Florin 

.4020 

Norway 

Gold 

Crown 

.2680 

Panama 

Gold 

Balboa 

1.0000 

Philippine  Islands   .     .     . 

Gold 

Peso 

.5000 

Portugal 

Gold 

Escudo 

1.0800 

Russia 

Gold 

Ruble 

.5150 

Spain 

Gold  and  silver 

Peseta 

.1930 

Sweden 

Gold 

Crown 

.2680 

Switzerland 

Gold 

Franc 

.1930 

Venezuela 

Gold 

Bolivar 

.1930 

BUS.    ARITH. 


16 


242  APPENDIX 

SQUARE  ROOT 

The  square  root  of  a  number  is  one  of  the  two  equal  fac- 
tors of  that  number. 

Find  the  square  root  of  16796.16. 

'  1'67'96.16'     |129.6  Point  off  the  number  into  periods  of 

2  two  places  each,  beginning  at  the  decimal 

point.  Find,  by  inspection,  the  perfect 
square  in  1,  the  first  period,  and  place 
it  in  the  root.  Square  1,  the  figure  al- 
ready found,  and  place  the  result  under  1, 
the  first  period.  Subtract  this  square 
from  the  first  period,  and  bring  down  the 
next  period,  67. 

Double  1,  the  root  already  found,  and 
place  the  result  at  the  left  of  67  as  a  trial  divisor.  2  will  be  contained 
in  6,  the  trial  dividend  of  67,  3  times.  If  we  place  this  3  in  the  trial 
divisor  and  in  the  root  and  multiply,  the  result,  69,  cannot  be  subtracted 
from  67,  so  we  must  use  2  as  the  second  figure  in  the  root.  Place  2  in  the 
root  and  in  the  trial  divisor,  and  multiply  as  shown.  Write  the  result, 
44,  under  the  67,  subtract,  and  to  the  remainder  (23)  bring  down  the 
next  period  of  the  number  (96).     2396  will  be  the  new  dividend. 

Double  the  root  already  found,  divide  24  into  239,  put  9  in  the  root 
and  in  the  divisor,  and  multiply.  Subtract  2241  from  2396.  To  the  re- 
mainder bring  down  the  next  period.  Double  129,  divide  258  into  1551, 
put  6  in  the  root  and  in  the  divisor,  and  multiply. 

The  decimal  point  is  placed  after  the  9  in  the  root  because  the  integers 
have  all  been  used  when  9  is  obtained  as  a  figure  of  the  root. 

Note.  The  square  root  of  a  fraction  is  obtained  by  extracting  the 
square  root  of  both  numerator  and  denominator;  e.g.y  V^^  =  f.  Or, 
change  the  fraction  to  a  decimal  and  extract  as  above. 


22  ~ 

67 
i4 

249 

2396 
2241 

2586 

15516 
15516 

ABBREVIATIONS   USED   IN   BUSINESS 


A.     . 

.     acre;  acres 

dr.    .     . 

debit 

ace.  or  %   account 

dr.    .     . 

debtor 

alt.  or  h.   altitude 

ea.    .     . 

each 

amt. 

.     amount 

e.g.  .     . 

for  example 

@     • 

.     at 

etc.  .     . 

and  so  forth 

av.   . 

.    average 

ex.   .     . 

example 

bal. 

.     balance 

exch.    . 

exchange 

bbl. or brl. barrel;  barrels 

f.      .     . 

franc 

bdl.  . 

.     bundle  ;  bundles 

far.  .     . 

farthing 

bg.  .     . 

,     bag;  bags 

f.o.  b.  . 

free  on  board 

bl.    . 

.     bale  ;  bales 

frt.  .     . 

freight 

B/L 

.     bill  of  lading 

ft.  or  '  . 

foot;  feet 

bot.  .     . 

,     bought 

gal..     . 

gallon;  gallons 

br't  for'd  brought  forward 

gi.    .     . 

gill;  gills 

bu.   .     , 

.     bushel;  bushels 

gr.    .     . 

gross 

bx.   .     , 

,     box;  boxes 

h      .     . 

hypotenuse 

cd.    .     , 

.     cord;  cords 

hhd.      . 

hogshead 

chg. 

.     charge 

hr.    .     . 

hour;  hours 

ck.   .     , 

.     check 

i.e.  .     . 

that  is 

c/o  . 

.     care  of 

in.  or  " 

inch ;  inches 

CO.      . 

.     company 

ins.  .     . 

insurance 

c.  0.  d. 

.     collect  on  delivery 

inst.      . 

present  month 

coll.      , 

.     collection 

int.  .     . 

interest 

com. 

.     commission 

Kork 

area 

cr.    . 

.     credit ;  creditor 

£      .     . 

pound  sterling 

cs.    .     , 

case;  cases 

lb.    .     . 

pound;  pounds 

ct.  or  ^ 

cent;  cents 

L.  C.  D. 

least  common  denominator 

ctg.  .     . 

,     cartage 

L.C.M. 

least  common  multiple 

cu.    .     , 

,    cubic 

ltd.  .     . 

limited 

cwt. 

,    hundredweight 

M.    .     . 

mark 

d.    .  . 

,    pence 

m.    .     . 

mill ;  miUs 

da.  .     . 

day;  days 

mdse.  . 

merchandise 

dft.  .     . 

draft 

mi.  .     . 

mile ;  miles 

disc.      . 

discount 

min.  or  ' 

minute;  minutes 

doz. .     . 

dozen 

mo.  .     . 

month;  months 

243 


244 


ABBREVIATIONS  USED  IN  BUSINESS 


mortg. 

mortgage  ■ 

rec't     . 

receipt 

no.  or  # 

number 

ren'd    . 

rendered 

o.k.      . 

all  correct 

rm. 

ream 

oz.    .     . 

ounce ;  ounces 

ry.  .     . 

railway 

p.    .   . 

page 

s.     .     . 

shilling;  shillings 

pay't    . 

payment 

sec.  or  " 

second;  seconds 

pc.   .     . 

piece 

sec. 

section;  sections 

pd.  .     . 

paid 

sq.  .     . 

sfjuare 

%     .     . 

per  cent 

St.  ht. 

slant  height 

pfd.      . 

preferred 

T.    .     . 

ton;  tons 

pkg.      . 

package 

twp.     . 

township 

pp.  .    . 

pages 

ult.       . 

last  month 

pr.    .    . 

pair;  pairs 

via       . 

by  way  of 

prox.    . 

next  month 

viz. 

namely 

pt.   .     . 

pint;  pints 

vol. 

volume 

pwt.      . 

pennyweight 

wk.      . 

week;  weeks 

qr.    .     . 

quire;  quires 

wt.  .     . 

weight 

qt.    .     . 

quart;  quarts 

yd..    . 

yard;  yards 

rd.   .     . 

rod;  rods 

yr.  .    . 

year;  years 

rec'd    . 

received 

INDEX 

(The  figures  refer  to  pages.) 


A.  B.  A.  checks,  204 
Abbreviations,  243 
Above  par,  192 
Acceptance,  206 
Account,  checking,  158 

purchase   134 

sales,  134,  136 

savings,  159 
Acre,  68 
Addition,  7 

checking,  12 

denominate  numbers,  73 

fractions,  51 

horizontal,  14 
Ad  valorem  duty,  183 
Agate,  72 
Aliquot  parts,  47 
Altitude,  93,  97 
Amount,  117,  144 
Angle,  92 
Annuity,  155 
Anticipation,  125 
Apothecaries'  fluid  measure,  70 

weight,  66 
Apportionment,  181 
Approximate  measures,  107 
Approximations,  107 
Arbitrage,  211 
Area,  93 

of  circle,  95 

of  parallelogram,  94 

of  triangle,  94 
Assessment,  stock,  192 

tax,  180 
Assessors,  180 
Avoirdupois  weight,  64 

Balance,  158 
Balancing  account,  20 
Bale,  72 
Bank,  157 

check,  157,  161,  203 

discount,  164 

draft,  203 

Federal  reserve,  158 

National,  157 

note,  64,  157 

private,  158 

savings,  158 

state,  158 


Barrel,  66,  70 
Base,  line,  68,  117 

in  mensuration,  93 

in  percentage,  117 
Below  par,  192 
Beneficiary,  189 
Bill,  clean,  210 

documentary,  210 

of  exchange,  210 
Board  foot,  104 
Bond,  196 

coupon,  196 

registered,  198 

table,  198 
Bricks,  105 

Broker  commission,  133 
Brokerage,  133,  193 
Building  and  Loan  Associations,  164 
Bundle,  72 
Bushel,  70 

Cable  transfer,  209 
Canadian  money,  64 
Cancellation,  42 

interest  method,  146 
Capital,  213 

loans,  163 
Carat,  66 
Carload  lots,  215 
Carpeting,  100 
Cash  discount,  124 
Cashier's  check,  204 
Cask,  66 

Casting  out  9's,  12,  24,  29 
Cent,  63 
Cental,  66 
Centime,  64 
Century,  71 
Certificate,  coupon,  196 

of  deposit,  160 

stock,  193 
Certified  check,  203 
Chain,  68 
Check,  A.B.A.,  204 

accuracy,  12,    18,  24,  29 

bank,  161,  203   , 

cashier's,  204 

certified,  203 

travelers',  204 
Checking  account,  158 
245 


246 


INDEX 


Circle,  71,  93 
Circular  measure,  71 
Circumference,  93 
Class  rates,  215 
Clean  bills,  210 
Clearing  house,  209 
Closed  policy,  185 
Coins,  Canada,  64 

United  States,  63 
Coinsurance,  187 
Collateral,  162 

notes,  162 
Collection  charge,  203 
Collector,  133 

Combinations  in  addition,  7 
Commercial,  discount,  123 

draft,  204 

fractions,  55 

time  table,  71 

weight,  64 
Commission,  133,  193 

merchant,  133 
Commodity  rates,  215 
Common,  divisor,  40 

fraction,  43 

interest,  144 

multiple,  41 

stock,  193 
Complement,  18 
Compound  interest,  153 

subtraction,  106 

time,  106 
Cone,  97 
Consignee,  134 
Consignment,  134 
Consignor,  134 
Cord,  69 
Corporation,  192 

tax,  180 
Cost,  first  or  prime,    130 

gross,  120 

net,  120 
Counting  table,  72 
Coupon,  bond,  196 

certificate,  196 
Credit,  157 
Cube,  39,  96 
Cubic  measure,  69 
Customs,  183 
Cylinder,  97 

Date  of  maturity,  164 
Day,  71 

of  grace,  164 
Decimal,  43 

point,  60 
Decime,  64 
Degree,  71 

Denominate  numbers,  63 
Denomination,  198 


Denominator,  43 

least  common,  46 
Deposit,  158 

certificate  of,  203 

slip,  158 
Depositor's  ledger,  20 
Diagonal,  93 
Diameter,  93 
Diamond  weight,  66 
Difference,  in  time,  106 

in  percentage,  117 
Discount,  bank,  162,  164 

commercial,  123 

series,  127 

time,  164 

true,  168 
Divisibility  tests,  38 
Division,  28 
Divisor,  greatest  common,  40 

in  fractions,  58 
Documentary  bills,  210 
Dollar,  63 
Dozen,  72 
Draft,  acceptance,  206 

bank,  203 

commercial,  205 

sight,  206 

time,  206 
Dram,  65,  67 
Drawee,  205 
Drawer,  205 
Dry  measure,  70 
Duty,  183       '• 

Eagle,  63 

Endowment  policy,  189 

English  money,  64 

Equalizing  investment,  214 

Equation,  88 

Even  number,  38 

Exact  interest,  151 

time  table,  166 
Exchange,  201 

bUl  of,  210 

cost  of,  209 

domestic,  201 

foreign,  201,  209 

indirect,  210 

par  of,  210,  211 

rate  of,  201,  211,  212 
Exponent,  39 
Express  money  order,  202 

Factor,  38 

method,  44 
Factoring,  38 
Farthing,  64 
Fathom,  67 

Federal  reserve  bank,  158 
Fee,  202 


INDEX 


247 


Fire  insurance,  185 
Firkin,  66 
Flooring,  103 
Foot,  67 

board,  104 
Footing,  14 

Formulas,  94,  98,  118,  121 
Fractions,  43 
Franc,  64 
Free  list,  183 
Freight,  rates,  215 

tariff,  215 
French  money,  64 
Fund,  157 

sinking,  155 
Furlong,  67 

Gain  and  Loss,  120 

Gallon,  70 

G.  C.  D.  method,  44 

Geographical  mile,  67 

German  money,  64 

GUI,  70 

Gold,  certificates,  64 

coins  U.  S.,  63 

fineness  of,  66 
Government,  land  measure,  68 

money,  63 
Grain  measure,  66,  67 
Graph,  79 

Greatest  common  divisor,  40 
Great  gross,  72 
Gross,  72 

cost,  120,  134 

proceeds,  134 

weight,  66 
Guaranty,  134 
Gunter's  chain,  68 

Hand,  67 

Heaped  bushel,  70 
Horizontal  addition,  14 
Hour,  71 

Hundredweight,  65 
Hypotenuse,  92 

Import  duties,  183 
Improper  fraction,  45 
Inch,  67 
Income  tax,  180 
Incorporated  companies,  192 
Indemnify,  185 
Indirect  exchange,  210 
Indirect  tax,  180,  183 
Indorsement,  161 
Industrial  loans,  163 
Inheritance  tax,  180 
Insolvency,  213 
Insurance,  185 
fire,  185 


life,  189 

table  of,  190 
Interchange  of  fractions,  43 
Interest,  144 

bearing  debts,  144 

cancellation  method,  145 

common,  144 

compound,  153 

exact,  151 

formulas,  144 

laws,  144 

6  per  cent  method,  148 

60-day  method,  147 

special  methods,  151 
Investment  loans,  163 
Invoice,  date  of,  124 

Joint  rate  commission,  215 
Judgment  notes,  162 

Karat,  66 
Keg,  66 
Knot,  67 

Land  measure,  68 

League,  67 

Leakage,  183 

Least  common  denominator,  46 

Least  common  multiple,  41 

Legal  rate  of  interest,  144 

Letter  of  credit,  210 

Liabilities,  122,  213 

License  fee,  180 

Line,  92 

Linear  measure,  67 

Link,  68 

Liquid  measure,  70 

Load,  69 

Loans,  162 

London  exchange,  202 

Long  measure,  67 

Long-time  loans,  163 

Long  ton,  65 

Loss,  213 

Lumber  104 

Making  change,  18 
Manual  training,  107 
Mark,  64 

Market  value,  192 
Marking  goods,  128 
Maturity,  144 
Measures,  of  capacity,  64 

of  value,  63 

of  weight,  64 
Mensuration,  92 
Merchants'  rule,  171 
Meridian,  principal,  68 
Metric  system,  237 
Mile,  67,  68 


248 


INDEX 


Mill,  63 

Minimum  weight,  216 

Minute,  circular  measure,  71 

time  measure,  71 
Miscellaneous,  measures,  72 

problems,     30,    83,    109,    137, 
221 
Mixed  number,  45 
Money,  centers,  202 

tables,  63 
Month,  71 
Mortgage  loans,  163 
Multiplication,  23 

of  commercial  fractions,  55 

of  fractions,  53 

rapid  method  of,  25 

National  Bank,  157 
Negotiable  paper,  162 
Net  cost,  120 

gain,  213 

loss,  213 

price,  124 

proceeds,  134 

selling  price,  121 

weight,  66 

wholesale  price,  124 
New  York  exchange,  202 
Nonnegotiable  paper,  162 
Note,  collateral,  162 

judgment,  162 
Numerator,  43 

Open  policy,  185 
Ounce,  apothecaries',  67 

commercial,  65 

Troy,  66 

Painting,  100 
Papering,  100 
Par,  192 

of  exchange,  210 

value,  192 
Parallel  lines,  92 
Parallelogram,  93 
Parcel  post,  219 
Parenthesis,  18 
Partial  payments,  169 
Partnership,  213 
Pass  book,  158 
Peck,  70 
Pence,  64 
Pennyweight,  66 
Percentage,  117 
Perch,  69 
Perimeter,  93 
Perpendicular,  92 
Pfennig,  64 
Pica,  72 
Pint,  70 


172, 


Plastering,  100 
Point,  72 
Policy,  185 

endowment,  189 

open,  185 

term,  189 

valued,  185 

whole  life,  189 
Poll  tax,  182 
Polygon,  92 
Postal,  money  order,  202 

savings  bank,  162 

savings  certificate,  162 
Pound,  commercial,  65 

Troy,  66 

sterling,  64 
Power,  39 

Practical  measurements,  100 
Preferred,  risk,  187 

stock,  193 
F*remium,  insurance,  185 

stock,  192 
Present  worth,  168,  213 
Price,  list,  124 

net,  124 
Prime  cost,  134 

factor,  38 

number,  38 
Principal,  134,  144 

meridian,  68 
Printers'  measure,  72 
Prism,  96 
Private  bank,  158 
Proceeds,  bank,  164 

gross,  134 

net,  134 
Profit,  130,  213 
Proper  fraction,  45 
Properties  of  numbers,  38 
Property  tax,  180 
Protest,  206 
Pyramid,  97 

Quadrilateral,  92 
Quart,  70 
Quintal,  66 
Quire,  72 

Radical  sign,  40 
Radius,  93 
Railroad,  215 
Range,  68 
Rate,  carload,  215 

class,  215 

commodity,  215 

exchange,  201 

legal  interest,  144 

per  cent,  117,  144 

railroad,  215 
Ream,  72 


INDEX 


249 


Reciprocal,  58 
Rectangle,  93 
Reduction,  of  denominate  numbers,  73 

of  fractions,  44 
Registered  bond,  198 
Resources,  122,  213 
Retail  merchants'  table,  131 
Review  problems,  227 
Right  angle,  92 

triangle,  92 
Road  taxes,  180 
Rod,  67,  68 
Roofing,  103 
Root,  square,  242 

Savings  bank,  158,  162 

Score,  72 

Scruple,  67 

Second,  circular  measure,  71 

time  measure,  71 
Section  of  land,  69 
Security,  162 
Share,  192 
Sheet,  72 
Shilling,  64 
Shipment,  134 
Short  rate,  187 
Short-time  loans,  163 
Sight  draft,  206 
Simple  interest,  144 

table,  149 
Sinking  fund,  155 
Six  per  cent  method,  148 
Sixty-day  method,  147 
Size,  67 

Slant  height,  97 
Solar  year,  71 
Solids,  96 
Sovereign,  64 

Special  interest  methods,  151 
Specific  duty,  183 
Square,  68,  93 

measure,  68 

roofing,  103 

root,  40,  242 
Standard  time,  71 
State  bank,  158 
Statute  mile,  67 
Stocks,  192 

assessment,  192 

broker,  193 

certificate,  192 

common,  193 

companies,  192 

preferred,  193 
Stone,  105 
Stub  of  check,  161 
Subsidiary  coins,  64 
Substitution,  89 
Subtraction,  17 


checking,  18 

compound,  106 

fractions,  52 
Surface  measure,  68 
Surveyors'  long  measure,  68 

Tables,  aliquot  parts,  47 

bond,  198 

commercial,  65 

compound  interest,  154 

counting,  72 

denominate  numbers,  63 

domestic  exchange,  202 

foreign  coins,  241 

foreign  exchange,  211,  212 

import  duties,  183 

insurance,  190 

metric  system,  237 

miscellaneous  measures,  72 

money,  63 

multiplication,  23 

paper,  72 

parcel  post,  219 

percentage,  47 

printers',  72 

retail  merchants',  131 

simple  interest,  149 

sinking  fund,  155 

time,  166 
Tare,  66,  183 
Tariff,  180 

freight,  215 
Tax,  180 

apportionment,  181 

assessment,  180 

direct,  180 

formulas,  180 

indirect,  180,  183 

transfer,  200 
Telegraphic  money  order,  202 
Teller,  158 
Term,  fraction,  43 

of  credit,  124 

policy,  189 
Tests  of  divisibility,  38 
Time,  144 

discount,  164 

draft,  206 

measure,  71 

standard,  72 

table,  166 
Ton,  65 
Township,  69 
Trade  discount,  123 
Transfer,  of  money,  201 

tax,  200 
Travelers'  checks,  204 
Trial  balance,  35 
Triangle,  92 
Troy  weight,  66 


250 


INDEX 


True  discount,  168,  192,  194 
Trust  companies,  158 
Two-figure  combinations,  7 

United  States,  customs,  183 

money,  63 

rule,  170 
Usury,  144 

Value,  of  foreign  coins,  241 

insurable,  186 

market,  192 

par,  192 
Valued  policy,  185 
Vinculum,  18 
Volume,  97 


Week,  71 

Weight,  apothecaries',  66 

commercial,  64 

Troy,  66 
Whole-life  policy,  189 
Wholesale  and  retail  profits, 
Winchester  bushel,  70 
Withdrawals,  160 
With  exchange,  205 
Without  exchange,  205 
Wood,  105 

Yard,  67 
Year,  71 

Zone,  220 


130 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  50  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.00  ON  THE  SEVENTH  DAY 
OVERDUE. 


SEP  2519*1 


l5Dec'521K 


DEC  18 1952  i; 


MAR  5  19423 


iSDec'KOLt 


•WTTjseo 


AUG  11    1944 


>^     >. 


05 


NriVl4B6B 


13Jec'£0Lf 


LD  21-100m-7,'40 (69368) 


VB  1 7221' 


y 


30S986 


UNIVERSITY  OF  CAUFORNIA  UBRARY 


